Question

exponential models guided practice 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. example 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= done

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 (as a decimal), and $t$ is the time in years.

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

The initial value of the computer \(a = 6500\) (in dollars). The depreciation rate is \(14.3\% = 0.143\), so the decay factor \(1 - r = 1 - 0.143 = 0.857\).

Step3: Write the function

Substitute \(a = 6500\) and \(1 - r = 0.857\) into the exponential decay formula. So the function that models the value of the computer over time \(t\) (in years) is $y = 6500(0.857)^t$.

Answer:

$y = 6500(0.857)^t$