Question

The value of a textbook is $65 and decreases at a rate of 14% per year for 13 years.The exponential function that models the situation is?After 13 years, the value of the textbook is?

Answer 1

ANSWER

$\begin{gathered} A=65(1-0.16)^{13} \\ A\text{ = \ 6.74} \end{gathered}$

EXPLANATION

The initial value of the textbook is given as $65 and it decreases at a rate of 14% per year for 13 years.

Since this is an exponential function, it will be in the form:

$A\text{ = P(1 - }\frac{R}{100})^t$

where P = initial value

R = rate

t = time elapsed

A = amount after time t

From the question:

P = $65

R = 16%

t = 13 years

Therefore, the exponential function that models the situation is therefore:

$\begin{gathered} A\text{ = 65(1 - }\frac{16}{100})^{13} \\ A=65(1-0.16)^{13} \end{gathered}$

Therefore, the value of the textbook after 13 years is:

$\begin{gathered} A=65(0.84)^{13} \\ A\text{ = \ }6.74 \end{gathered}$

That is the value after 13 years.