Question

The table below shows the average value of houses in Wilshire Woods over a period of 5 years. The equation f(x) = 20,000 • 3x describes the curve of best fit for the average value of houses f(x). Let x represent the number of years since 2000, so x = 0 in 2000.

Year Average Home
Value
2000 $19,000
2001 $60,000
2002 $182,000
2003 $540,000
2004 $1,621,000
Using the equation for the curve of best fit, what will be the average home value in Wilshire Woods in 2005?

A.
$36,450,000
B.
$12,154,000
C.
$4,860,000
D.
$750,000

Answer 1

To calculate the average home value in Wilshire Woods for the year 2005 using the function f(x) = 20,000 • 3^x, set x to 5. The resulting calculation gives f(5) = 20,000 • 3^5 = 4,860,000, indicating the average home value will be $4,860,000.

Step-by-step explanation:

The student is asking for the calculation of the average home value in Wilshire Woods for the year 2005 using the provided exponential growth function f(x) = 20,000 • 3x, where x represents the number of years since 2000. To find the value of f(x) for the year 2005, we set x to 5, since 2005 is 5 years after 2000.

The calculation would be:

f(5) = 20,000 • 35 = 20,000 • 243 = 4,860,000.

Therefore, the average home value in Wilshire Woods in 2005, according to the curve of best fit, would be $4,860,000.