Question

exponential models
a computer valued at $6500 in 2007 depreciates at the rate of 14.3%
per year.
this situation can be modeled using an exponential decay function.
type your answer and then click or tap done.
use the ^ symbol (shift+6 on the keyboard) to signify an exponent. for
example, for 2 to the third power, enter 2^3.
write a function that models the value of the computer.
y=
©sebastian kaulitzki/shutterstock, ©marie c fields/shutterstock
a computer can depreciate 14.3% per year.

Explanation:

Step1: Recall the exponential decay formula

The general form of an exponential decay function is $y = a(1 - r)^t$, where $a$ is the initial amount, $r$ is the rate of decay (in decimal form), and $t$ is the time (in years, in this case).

Step2: Identify the values of \(a\) and \(r\)

• The initial value of the computer (\(a\)) is $6500$ (the value in 2007).
• The rate of depreciation (\(r\)) is $14.3\%$, which in decimal form is $0.143$.

Step3: Substitute the values into the formula

Substitute \(a = 6500\) and \(r = 0.143\) into the exponential decay formula:
\(y = 6500(1 - 0.143)^t\)
Simplify \(1 - 0.143 = 0.857\), so the function becomes \(y = 6500(0.857)^t\).

Answer:

$y = 6500(1 - 0.143)^t$ (or $y = 6500(0.857)^t$)