Question

a table of values for the exponential function \\(f\\) is shown below. the values represent the value of a car over a period of 5 years since it was purchased.

\\(\

$$\begin{array}{|c|c|} \\hline x & y \\\\ \\hline 0 & 25,500 \\\\ \\hline 1 & 21,675 \\\\ \\hline 2 & 18,424 \\\\ \\hline 3 & 15,660 \\\\ \\hline 4 & 13,311 \\\\ \\hline 5 & 11,314 \\\\ \\hline \\end{array}$$

\\)

use an exponential regression to determine a function for this data.

a. \\(y = 21675(0.85)^x\\)
b. \\(y = 25500(0.85)^{x-1}\\)
c. \\(y = 25500(0.85)^x\\)
d. \\(y = 21675(1.15)^x\\)

Explanation:

Identify the initial value

Using the Exponential Functions knowledge point

$$
LATEXBLOCK0
$$

Determine the decay factor

Using the Exponential Decay knowledge point

$$
LATEXBLOCK1
$$

Formulate the regression equation

Using the Exponential Functions knowledge point

$$
LATEXBLOCK2
$$

Answer:

• A. \(y = 21675(0.85)^x\)
• B. \(y = 25500(0.85)^{x-1}\)
• C. \(y = 25500(0.85)^x\) (Correct answer)
• D. \(y = 21675(1.15)^x\)