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Write an exponential function to model the situation. The value of a car is
$18000 and is depreciating at a rate of
12% per year.

V(t)=18000(.88)^(t)

V(t)=.88(18000)^(t)

V(t)=.12(18000)^(t)

V(t)=18000(.12)^(t)

Write an exponential function to model the situation. The value of a car is $\$ 18000$ and is depreciating at a rate of $12 \%$ per year. $\newline$ $V(t)=18000(.88)^{t}$ $\newline$ $V(t)=.88(18000)^{t}$ $\newline$ $V(t)=.12(18000)^{t}$ $\newline$ $V(t)=18000(.12)^{t}$

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Write exponential functions: word problems

Full solution

Q. Write an exponential function to model the situation. The value of a car is

\$ 18000

and is depreciating at a rate of

12 \%

per year.

\newline

V(t)=18000(.88)^{t}

\newline

V(t)=.88(18000)^{t}

\newline

V(t)=.12(18000)^{t}

\newline

V(t)=18000(.12)^{t}

Identify Values: Identify the initial value $a$ and the rate of depreciation $r$ . The initial value of the car is $\$18,000$ , which is the value when $t = 0$ . The rate of depreciation is $12\%$ per year, which means the car loses $12\%$ of its value each year.
Convert to Decimal: Convert the rate of depreciation to a decimal. $\newline$ To convert a percentage to a decimal, divide by $100$ . $\newline$ $12\%$ as a decimal is $\frac{12}{100} = 0.12$ .
Determine Decay Factor: Determine the decay factor $b$ . Since the car is depreciating, we subtract the rate of depreciation from $1$ to find the decay factor. $b = 1 - r$ $b = 1 - 0.12$ $b = 0.88$
Write Exponential Decay Function: Write the exponential decay function. $\newline$ The general form of an exponential decay function is $V(t) = a(b)^t$ , where $V(t)$ is the value after $t$ years, $a$ is the initial value, and $b$ is the decay factor. $\newline$ Substitute the values of $a$ and $b$ into the equation. $\newline$ $V(t) = 18000(0.88)^t$

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