Kwan's parents bought a home for $50,000 in 1997 just as real estate values in the area started to rise quickly. Each year, their house was worth more until they sold the home for $309,587. Model the growth of the home's value from 1997 to 2007 with both linear and an exponential equation. Graph the two models below.
Answers
A. First let us start with the linear model.
The equation is in the form of y = m x + b
Calculating for the slope m:
m = (309,587 – 50,000) / (2007 – 1997)
m = 25,958.7
Subsituting:
y = 25,958.7 x + b
Taking x = 1997, y = 50,000. Solve for b:
50,000 = 25,958.7 (1997) + b
b = -51,789,523.9
The complete equation is therefore:
y = 25,958.7 x - 51,789,523.9
B. The exponential model has the following form:
y = a b^x
where a and b are constants
Taking x1= 1997, y1 = 50,000; x2 = 2007, y2 = 309,587
50,000 = a b^1997
309,587 = a b^2007
Combining in terms of a:
50,000 / b^1997 = 309,587 / b^2007
b^2007 / b^1997 = 309,587 / 50,000
b^10 = 6.19174
b = 1.2
Substituting:
y = a 1.2^x
Solving for a:
50,000 = a 1.2^1997
a = 3.75 x 10^-154
The complete equation is:
y = 3.75 x 10^-154 * 1.2^x
Related Questions
What is the term for a descriptive value found by using data from a census?
choices are....
Statistics
Parameter
Mean
Median
Mode
Answers
Answer:
Parameter
Step-by-step explanation:
Enter the values to complete the statement. To determine whether (−1,4) (−1,4) is a solution to the equation 3x+8y=29 3x+8y=29 , substitute for x and and for y
Answers
In a pair of values like (-1, 4), the first coordinate, or entry, occupied by -1 always represents x.
Similarly, the second coordinate occupied by 4 represents y.
Answer: substitute ...-1... for x and ...4... and for y.
Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a tip of $5. Ann paid a total of $49.10
Write an equation to determine the distance in miles (x) between the airport and Ann's home.
Write an equation to determine the distance in miles (x) between the airport and Ann's home.
Answers
2.1*d+5=49.10 solve for d
d=49.10-5/2.1 = 21 miles
did 6600 bee come first or did 2500 bce
Answers
Carlene is selling T-shirts for a fundraiser. The T-shirts cost $20.50 each. To date, she has raised $700. Her goal is to raise more than $8,900. How many more T-shirts, x, does Carlene need to sell to reach her goal?
Answers
Divide 700 by 20.5. This will give you the amount of shirts she has already raised with is 36 (more accurately 36 6/41). Next divide 8900 by 20.5. This is the amount of shirts she needs to sell in total, which is 434. Subtract these two values.
Hope this helps
Carlene needs to sell 400 more T-shirts at $20.50 each to reach her goal of raising more than $8,900, after already raising $700.
The question asks us to determine how many more T-shirts, designated as x, Carlene needs to sell to reach her fundraising goal of more than $8,900, given that each T-shirt costs $20.50 and she has already raised $700. To solve for x, we can set up the following equation:
Total goal - Amount already raised = Amount still needed
$8,900 - $700 = $8,200
Next, we divide the amount still needed by the price per T-shirt to find out how many T-shirts need to be sold:
x = Amount still needed / Price per T-shirt
x = $8,200 / $20.50
x = 400
Carlene needs to sell 400 more T-shirts to reach her goal.
A transversal must intersect two or more _____ lines.
Answers
if a transversal intersects two lines that are corresponding then the angles are congruent so the lines are parallel.
(this is learned in (9th grade Geometry) refer to books for more rules and theorems
Answer:
paralell lines, i think.
Step-by-step explanation:
What is the rational exponent expression of 3 square root 4n
Answers
4 and one half divided by 3
ANSWER ASAP!!
Answers
What is the domain of this relation?
{ (-1,5), (4,1), (8,3), (4,5) }
Answers
In this case, just take all the x values. They are:
-1, 4, 8, and 4.
Of course, there are no repeats with domain values.
So the domain set would just be -1, 4, and 8.
Or the last choice,
{-1, 4, 8}
A box contains 12 1/2 square feet of tiles and costs $40.21 what is the approximate price per square foot
Answers
The approximate cost per square foot for the tiles is $3.22 when rounded to the nearest cent.
To calculate the price per square foot of tiles, divide the total cost of the tiles by the total number of square feet. The total cost given is $40.21, and the total area is 12 1/2 square feet.
First, convert the mixed number to an improper fraction. 12 1/2 is the same as 25/2 square feet. Now, to find the cost per square foot, perform the following division:
Price per square foot = Total cost / Total area in square feet
Price per square foot = $40.21 / (25/2 square feet)
Multiply by the reciprocal:
Price per square foot = $40.21 / 1 x 2 / 25
Price per square foot = $40.21 x 2 / 25
Price per square foot = $80.42 / 25
Price per square foot = $3.2168
Therefore, the approximate cost per square foot for the tiles is $3.22 when rounded to the nearest cent.
The approximate price per square foot is $3.22.
To find the price per square foot, divide the total cost by the total square footage. In this case, the cost is $40.21 and the square footage is 12 1/2 square feet.
1. Cost per square foot = Total cost / Total square footage
2. Cost per square foot = $40.21 / 12.5 sq ft ≈ $3.22/sq ft
1. Convert 12 1/2 square feet to a decimal: 12.5 sq ft.
2. Divide the total cost by the total square footage: $40.21 / 12.5 sq ft ≈ $3.22/sq ft.
To calculate the cost per square foot, you need to divide the total cost by the total square footage. In this case, the total cost is $40.21, and the total square footage is 12 1/2 square feet. First, convert 12 1/2 square feet to a decimal, which is 12.5 sq ft. Then, divide the total cost by the total square footage:
Cost per square foot = $40.21 / 12.5 sq ft ≈ $3.22/sq ft.
Therefore, the approximate price per square foot is $3.22.
complete question
A box contains 12 1/2 square feet of tiles and costs $40.21 what is the approximate price per square foot
Mary is 19 years old. she drinks the recommended intake of 2.2 liters of water and other beverages a day. about how many cups is this equivalent to?
Answers
To convert 2.2 liters to cups, multiply by 4.22675. Rounded, it's approximately 9 cups. So, option C) [tex]$9$[/tex] cups is correct.
To find out how many cups 2.2 liters is equivalent to, we'll first convert liters to cups.
1 liter is approximately equal to 4.22675 cups.
So, to find out how many cups are equivalent to 2.2 liters:
[tex]\[ \text{Number of cups} = 2.2 \, \text{liters} \times 4.22675 \, \text{cups/liter} \][/tex]
[tex]\[ \text{Number of cups} \approx 9.29885 \, \text{cups} \][/tex]
Rounded to the nearest whole number, 2.2 liters of water is approximately equivalent to 9 cups. Therefore, the correct answer is:
C) [tex]$9$[/tex] cups
The correct question is:
Mary is 19 years old. She drinks the recommended intake of 2.2 liters of water and other beverages a day. About how many cups is this equivalent to?
A) 3 cups
B) 6 cups
C) 9 cups
D) 12 cups
HELP THIS IS URGENT 40 POINTS
Josiah, the manager of a pet store, bought 72 oz of water conditioner to use in his fish tanks. His small tanks would require 2 oz of conditioner and his large tanks would require 6 oz of conditioner. He made a sketch to show the line representing the different combinations of tanks he could put the water conditioner into. The x-axis represented the number of small tanks and the y-axis represented the number of large tanks. The manager labeled only the intercepts.
Which points did the manager label?
(0, 6) and (2, 0)
(0, 12) and (36, 0)
(6, 0) and (0, 2)
(0, 36) and (12, 0)
Answers
A fair coin is tossed 9 times. what is the probability that the coin lands head at least 7 times?
Answers
Each member of a four-member relay team ran 100 meters during the relay. The time, in seconds, for each member is shown below. 13.9 s, 12.85 s, 14.82 s, 12.74 s Which expression finds the total time for the relay team?
Answers
Answer:
T = 13.9 + 12.85 + 14.82 + 12.74
Step-by-step explanation:
Great question, it is always good to ask away and get rid of any doubts that you may be having.
Based on the information in the question, the total time for the relay would be calculated by simply adding each of the four-relay members time during the 100 meter run. Therefore the expression would be
T = 13.9 + 12.85 + 14.82 + 12.74
T = 54.31 seconds.
If we decided to solve for the Total time (T) it would add up to 54.31 seconds for the relay time. But since the question did not ask for the total but just the expression. Then the answer is the expression above.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
A health food producer has 250 samples of a new snack to distribute in the mall the producer has to keep at least 50 samples for display in the health food store for the product launch how long will the samples last if consumers are taking the samples at a rate of 25 every hour
Answers
Final answer:
The 200 samples available for distribution will last for 8 hours at a consumption rate of 25 samples per hour.
Explanation:
The health food producer has 200 samples to distribute (250 total minus 50 for display), and if consumers take samples at a rate of 25 every hour, you would divide the 200 samples by the rate of 25 samples per hour to calculate how long the samples will last.
200 samples ÷ 25 samples/hour = 8 hours.
Therefore, the samples available for distribution at the mall will last for 8 hours before they run out, assuming the rate of consumption is constant at 25 samples per hour.
(1 point) find ∬rf(x,y)da∬rf(x,y)da where f(x,y)=xf(x,y)=x and r=[1,6]×[4,5]r=[1,6]×[4,5].
Answers
The double integral of the function f(x, y) = x over the rectangle defined by [1, 6] and [4, 5] is calculated through an iterated integral to be 17.5.
Explanation:The problem asks to find double integral of the function f(x, y) = x over the rectangle R defined by the interval [1, 6] for x and [4, 5] for y. To find this, we perform an iterated integral. The integral is setup as follows:
∬Rf(x,y)dA = ∫ from 1 to 6 ∫ from 4 to 5 x dy dx
We first integrate with respect to y which gives us: xy| from 4 to 5 = x(5) - x(4) = x.
Then, we integrate this result with respect to x which gives us: 0.5x²| from 1 to 6 = 0.5(6^2) - 0.5(1^2) = 17.5
So, ∬Rf(x,y)dA equals to 17.5
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Using the Rational Root Theorem, what are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x – 12?
-4/5 and 3/4
-4/5 and -3/4
-1, -4/5, 3/4 and 1
-1. -4/5, -3/4 and 1
Answers
Answer:
Option 1 is correct.
Step-by-step explanation:
The given polynomial is
[tex]f(x)=20x^4+x^3+8x^2+x-12[/tex]
we have to find all the rational roots of the polynomial f(x)
The Rational Root Theorem states that the all possible roots of a polynomial are in the form of a rational number i.e in the form of [tex]\frac{p}{q}[/tex]
where p is a factor of constant term and q is the factor of coefficient of leading term.
In the given polynomial the constant is -12 and the leading coefficient is 20.
[tex]\text{All possible factor of -12 are }\pm1,\pm2, \pm3, \pm4,\pm6,\pm12[/tex]
[tex]\text{All possible factor of 20 are }\pm1,\pm2,\pm4,\pm5,\pm10,\pm20[/tex]
So, the all possible rational roots of the given polynomial are,
[tex]\pm1,\pm2, \pm3, \pm4,\pm6,\pm12,\pm\frac{1}{2},\pm\frac{3}{2},\pm\frac{1}{4},\pm\frac{3}{4},\pm\frac{1}{10},\pm\frac{1}{5},\pm\frac{3}{5},\pm\frac{3}{10},\pm\frac{2}{5},\pm\frac{6}{5},\pm\frac{1}{20},\pm\frac{3}{20},\pm\frac{4}{5},\pm\frac{12}{5}[/tex]
Now, the rational roots of polynomial satisfy the given polynomial
[tex]f(-\frac{4}{5})=20(-\frac{4}{5})^4+(-\frac{4}{5})^3+8(-\frac{4}{5})^2-\frac{4}{5}-12=\frac{256}{625}\times 20-\frac{64}{125}+\frac{128}{125}-\frac{4}{5}-12[/tex]
[tex]=\frac{1024}{125}-\frac{64}{125}+\frac{128}{25}-\frac{4}{5}-12[/tex]
[tex]=\frac{960}{125}+\frac{128}{25}-\frac{4}{5}-12=12-12=0[/tex]
Hence, rational root.
[tex]f(\frac{3}{4})=20(\frac{3}{4})^4+(\frac{3}{4})^3+8(\frac{3}{4})^2+\frac{3}{4}-12=\frac{405}{64}+\frac{27}{64}+\frac{9}{2}+\frac{3}{4}-12=0[/tex]
rational root
[tex]f(1)=20(1)^4+(1)^3+8(1)^2+1-12=20+1+8-11=18\neq 0[/tex]
not a rational root.
hence, option 1 is correct
Answer:
The first option
Step-by-step explanation:
Right on edg:)
If f(x) is a continuous function defined for all real numbers, f(–10) = –2, f(–8) = 5, and f(x) = 0 for one and only one value of x, then which of the following could be that x value?
–7
–9
0
2
Answers
That is, f at -10 is negative, then at -8 is positive. So the graph of f "cuts" the x-axis for an x value in (-10, -8).
Since there is only one value such that f(x)=0, x can only be -9.
Answer: -9
The only value of x where f(x) = 0 can be determined by looking at the function's behavior near the x-axis and using the Intermediate Value Theorem. In this case, the potential x value is -9.
The one and only value of x where f(x) = 0 is the point of the function that intersects the x-axis. Since the function is continuous, it must cross the x-axis at this point due to the Intermediate Value Theorem.
To determine the possible value of x, we look at the given function values at x = -10 and x = -8 and identify where the function changes sign from negative to positive. The value of x where this sign change happens is the possible x value.
From the provided choices, the only value that would make this sign change possible is -9. Therefore, -9 could be the value of x where f(x) = 0.
four students volunteer at the hospital. Casey volunteers 20.7 hours,Danielle, two and three fourths, Javier 18 nine tenths, And Forrest twenty and eighteen twenty fiths who volunteerd the greatsest number of hours?
Answers
1. 20.7 hours Casey
2. Danielle 2 3/4 = 2.75 hours
3. Javier 18 9/10 = 18.9 hours
4. Forrest 20.72 hours
The length of a rectangular garden is 7 feet longer than its width. The garden's perimeter is 202 feet. Find the width of the garden.
Answers
Width: w
Perimeter: 202feet
Perimeter= l+l+w+w or 2l+2w
2(w+7)+2w=202
2w+14+2w=202
4w+14=202
-14 -14
4w = 188
/4 /4
w=47
The width of the garden is 47 feet
a car drives 630 miles on 35 gallons of gas. How far can it drive on 12 gallons?
Answers
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The car can drive 216 miles on 12 gallons.
What is displacement?The rate of change of position is called as displacement.
Now it is given that,
Distance traveled by car = 630 miles
Gas required to travel 630 miles = 35 gallons
Therefore, Distance travel n 1 gallon = Distance traveled by car / Gas required to travel 630 miles
⇒ Distance travel n 1 gallon = 630 / 35 miles
⇒ Distance travel n 1 gallon = 18 miles
Therefore, Distance travel n 12 gallon = 12 * Distance travel n 1 gallon
⇒ Distance travel n 12 gallon = 12 * 18 miles
⇒ Distance travel n 12 gallon = 216 miles.
Thus, the car can drive 216 miles on 12 gallons.
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The formula B=32A is used in New England to estimate the minimum furnace output, B, in BTUs, for a modern house with A square feet of flooring. Determine the minimum furnace output for a 1700 square foot modern house
Answers
Help super important
Based on the figure below, what is the value of x?
A. 5
B. 7
C. 11
D. 15
Answers
Taking a look at our screenshot provided, we can conclude that we need to find the missing angle degree out of 90 degrees, as we are dealing with a right angle.
Let's set this up as an Algebraic formula and solve for the variable;
5x + 15 + 50 = 90
First, let's combine like-terms (15 and 50).
5x + 65 = 90
Now, isolate our variable by subtracting 65 from each side of the equation.
90 - 65 = 25
65 - 65 = 0
5x = 25
Now, divide both sides by 5 to solve for x, our missing angle degree.
x = 5
Your answer is A.) 5
I hope this helps!
Madison is buying a $3,000 car at 9% simple interest for 2 years. What will be the total amount she pays for the car?
Answers
Answer:
3540.00
Step-by-step explanation:
The world record for the 24 hour run for women on all surfaces is 255.303 kilometers, set by mami kudo of Japan in 2011. What was her average speed?
Answers
The average speed of Mami on all surfaces is 10.64 km/hr.
What is average?Average is the mid value of two different higher and lower values. The average can be determined by taking the sum of all data and then dividing it by the number of data or the total value divided by the total no. of values.
Given a runner in 24 hours named Mami can run 255.303 kilometers on all surfaces.
∴ Her average speed is (255.303/24) km/hr.
= 10.64 km/hr.
∴ Her average speed is 10.64 km/hr all surfaces.
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I need help for all of these. Please give me all these answers, not just one please! :(
Answers
That's all I know sorry :(
Consider f and c below. f(x, y) = x2 i + y2 j c is the arc of the parabola y = 2x2 from (−1, 2) to (1, 2) (a) find a function f such that f = ∇f. f(x, y) = x3 3+ y3 3 correct: your answer is correct. (b) use part (a) to evaluate c ∇f · dr along the given curve
c.
Answers
In this exercise we have to perform the parameterization of the given function and we will have:
[tex]\int\limits_C {f} \, dr = f(1, 2)-f(-1, 2)= 2/3[/tex]
In there is some scalar function [tex]f(x, y)[/tex] such that:
[tex]\nabla f(x,y) = f(x, y) = x^2i+y^2j[/tex]
Then we want to find [tex]f[/tex] such that:
[tex]f'(x)= x^2= f(x,y) = \frac{x^3}{3} + g(y)\\f'(y)= y^2= f(x,y)= \frac{y^3}{3} + C\\f(x, y)= \frac{x^3}{3} +\frac{y^3}{3} + C[/tex]
So the vector filed [tex]f(x, y)[/tex] is conservative, which means the fundamental theorem applies; the line integral of [tex]f[/tex] along any path [tex]C[/tex] parameterized by some vector-valued function [tex]r(t)[/tex] over [tex]a\leq t\leq b[/tex] is given by:
[tex]\int\limits_C {f} \, dr\\\int\limits^t=a_t=b {f(r(t))} \, dt= f(r(b))-f(r(a))[/tex]
In the case:
[tex]\int\limits_C {f} \, dr = f(1, 2)-f(-1, 2)= 2/3[/tex]
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This problem requires calculation in multivariable calculus. Function f = ∇f when f(x, y) = x³/3 + y³/3. To calculate the line integral of ∇f · dr over the curve c, take the difference between the end and start points of the scalar function.
Explanation:The subject for this calculation is multivariable calculus, dealing with operations such as the gradient (∇) and line integrals.
According to the given function f(x, y) in part (a), it can be seen that f = ∇f for f(x, y) = x³/3 + y³/3. The vector field of this function is conservative since it corresponds to the gradient of a scalar function.
For part (b), you will need to calculate the line integral of ∇f · dr over the curve c, which is y = 2x² from (-1, 2) to (1, 2). The result of this will be the difference between the end and start points of the scalar function: f(1, 2) - f(-1, 2).
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Two weeks ago, Alice came home from vacation and noticed that a bean plant was growing in her garden. Today, the stalk is $452$ centimeters tall, and Alice observed that its height increases by $5\%$ every day. How tall was the plant $2$ weeks ago when she first noticed it growing? Express your answer as a decimal to the nearest tenth.
Answers
then 2 weeks go by, or 14 days, and the plant grew to 452 cm.
[tex]\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to 452\\ P=\textit{initial amount}\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ t=\textit{elapsed time}\to &14\\ \end{cases} \\\\\\ 452=P(1+0.05)^{14}\implies \cfrac{452}{1.05^{14}}=P[/tex]
Answer:
Te plant was 228.29 centimeters tall.
Step-by-step explanation:
To find the size of the plant 14 days (2 weeks ago), we will use a formula called "exponential growth."
[tex]A=P(1+r)^{t}[/tex]
where
A=accumulated amount.
P=initial ammount
r=rate
t=elapsed time.
replacing the values we have
A=452 centimeters
P=variable to find
r=5% = 0.05
t=2 weeks= 14 days
So, we substitute the values in the equation
[tex]452=P(1+0.05)^{14}[/tex]
Then, we clear the variable P
[tex]P=\frac{452}{1.05^{14} }[/tex]
and perform the operations
[tex]P=\frac{452}{1.979931} =228.29centimeters[/tex]
Last week, Marcus had a balance of - $10 in his savings account. This week, the balance is $10. Which equation would show the change,c, in his savings account...?
A. -10 + c =10
B. c + 10 =10
C. c + -10 =-10
D. -10 - c =-10
Answers
________________________________________________________
Explanation:
________________________________________________________
The beginning balance is: " -$10 ".
The "ending balance", or "current balance", is: "$10" .
_________________________________________________________
So, the beginning balance is a "negative value", or a "deficit".
To get the change, "c" ,
either: " 10 − c = -10 " ;
________________________________
or: " -10 + c = 10 " .
________________________________
Among the answer choices given, the correct answer choice provided is:
______________________________________________________
Answer choice: [A]: " -10 + c = 10 " .
______________________________________________________
How is .8333 as a fraction 5/6?
Answers
The decimal 0.8333 is equivalent to the fraction 2/3.
To convert the decimal 0.8333 to a fraction, follow these steps:
Step 1: Let x be the decimal value:
x = 0.8333
Step 2: Multiply both sides of the equation by 10000 to remove the decimal:
10000x = 8333.3
Step 3: Subtract x from both sides of the equation:
10000x - x = 8333.3 - 0.8333
9999x = 8332.4667
Step 4: Divide both sides of the equation by 9999 to isolate x:
x = 8332.4667 / 9999
Divide both the numerator and the denominator by their greatest common divisor, which is 3333:
x = (8332.4667 ÷ 3333) / (9999 ÷ 3333)
x = (2.49995) / 3
Now, the fraction as a whole number over the denominator:
x = 2 / 3
Therefore, the fraction is 2/3.
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