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A computer sells for
$900 and loses
30% of its value per year.
Write a function that gives the computer's value,
V(t),t years after it is sold.

V(t)=

A computer sells for $\$ 900$ and loses $30 \%$ of its value per year. $\newline$ Write a function that gives the computer's value, $V(t), t$ years after it is sold. $\newline$ $V(t)=\square$

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Interpret the exponential function word problem

Full solution

Q. A computer sells for

\$ 900

and loses

30 \%

of its value per year.

\newline

Write a function that gives the computer's value,

V(t), t

years after it is sold.

\newline

V(t)=\square

Identify values: Identify the initial value of the computer and the annual depreciation rate. $\newline$ The initial value of the computer is $\$900$ , and it loses $30\%$ of its value each year.
Convert to decimal: Convert the annual depreciation rate into decimal form. $\newline$ A $30\%$ loss in value can be represented as $0.30$ in decimal form.
Determine depreciation factor: Determine the depreciation factor for each year. $\newline$ Since the computer loses $30\%$ of its value each year, it retains $70\%$ of its value each year. To find the depreciation factor, subtract the decimal form of the loss from $1$ . $\newline$ Depreciation factor = $1 - 0.30 = 0.70$
Write function for value: Write the function for the computer's value after $t$ years. $\newline$ The computer's value after $t$ years, $V(t)$ , can be found by multiplying the initial value by the depreciation factor raised to the power of $t$ . $\newline$ $V(t) = \text{Initial value} \times (\text{Depreciation factor})^t$ $\newline$ $V(t) = 900 \times (0.70)^t$

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