Question

An event management company purchases a new van. The value of the van, x years after the purchase, is shown in the table.Which statement is true?A.The situation can be modeled by an exponential decay function with a percent change of -11%.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 -10%.

Answer 1

Given the table:

Time(years) 0 1 2 3

Value(dollars) 20,000 18,000 16,200 14,580

Let's determine the correct statement.

Here, we can see that as the time increases, the value decreases.

So, the situation can be modelled using a decay function.

Now, let's find the decay rate.

Apply the formula:

`y=a(1-r)^t`

Where:

a is the initial value.

y is the value in dollars at t, time.

r is the decay rate.

We have:

`y=20000(1-r)^t`

Now use any of the values to solve for r.

Plug in 18000 for y and 1 for t.

`\begin{gathered} 18000=20000(1-r)^1 \\ \\ 18000=20000(1-r) \\ \\ (18000)/(20000)=1-r \\ \\ 0.9=1-r \\ \\ r=1-0.9 \\ \\ r=0.1 \end{gathered}`

The decay rate is 0.1

Let's convert the rate to percent.

Percent change = 0.1 x 100 = 10%

Therefore, the situation can be modeled by an exponential decay function with a percent change of -10%.

ANSWER:

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