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Susan bought a new car in $2020$ for $\$48000$ . If the value of the car decreases by $11\%$ each year write an exponential modle for the value of the car. Then, estimate the cost of the car in the year $2023$ .

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Write exponential functions: word problems

Full solution

Q. Susan bought a new car in

2020

for

\$48000

. If the value of the car decreases by

11\%

each year write an exponential modle for the value of the car. Then, estimate the cost of the car in the year

2023

.

Identify values: Identify the initial value $a$ and the rate of decrease $r$ . The initial value of the car, $a$ , is $\$48,000$ . The car decreases in value by $11\%$ each year, so $r = -11\%$ or $-0.11$ .
Convert rate to factor: Convert the rate of decrease to the decay factor $b$ . The decay factor $b$ is calculated by subtracting the rate of decrease from $1$ . So, $b = 1 - r$ . $b = 1 - (-0.11)$ $b = 1 + 0.11$ $b = 1.11$ This is incorrect because we should be subtracting the rate of decrease, not adding it. Let's correct this. $b = 1 - 0.11$ $b = 0.89$

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