Question

5
select the correct answer.
an event management company purchases a new van. the value of the van, x years after the purchase, is shown in the table.

time (years)	0	1	2	3

which statement is true?
a. the situation can be modeled by an exponential decay function with a percent change of -10%.
b. the situation can be modeled by an exponential growth function with a percent change of 10%.
c. the situation can be modeled by an exponential growth function with a percent change of 11%.
d. the situation can be modeled by an exponential decay function with a percent change of -11%.

Explanation:

Step1: Check if it's exponential decay/growth

To determine if it's exponential, we check the ratio of consecutive values.
For \( x = 0 \) to \( x = 1 \): \(\frac{18000}{20000}=0.9\)
For \( x = 1 \) to \( x = 2 \): \(\frac{16200}{18000}=0.9\)
For \( x = 2 \) to \( x = 3 \): \(\frac{14580}{16200}=0.9\)
Since the ratio is constant (0.9) and less than 1, it's exponential decay.

Step2: Calculate percent change

Percent change formula: \((\text{New Value}-\text{Old Value})/\text{Old Value}\times100\)
Using \( x = 0 \) to \( x = 1 \): \(\frac{18000 - 20000}{20000}\times100=\frac{-2000}{20000}\times100=- 10\%\)

Answer:

A. The situation can be modeled by an exponential decay function with a percent change of -10%.