Question

exponential from two points (context)score: 0/1 penalty: nonequestionmagan purchased a new car in 2010 for $25,900. the value of the car has been depreciating exponentially at a constant rate. if the value of the car was $10,800 in the year 2014, then what would be the predicted value of the car in the year 2020, to the nearest dollar?watch videoshow examplesanswersubmit answer

Explanation:

Step1: Define exponential decay model

The standard exponential decay formula is $V(t) = V_0 \cdot r^t$, where:

• $V_0$ = initial value,
• $r$ = decay rate per year,
• $t$ = time in years since 2010.

Step2: Plug in 2014 values

For 2014, $t=4$, $V(4)=10800$, $V_0=25900$:
$10800 = 25900 \cdot r^4$

Step3: Solve for decay rate $r$

First isolate $r^4$:
$r^4 = \frac{10800}{25900} \approx 0.417$
Take 4th root to find $r$:
$r = \sqrt[4]{0.417} \approx 0.805$

Step4: Calculate 2020 value

For 2020, $t=10$:
$V(10) = 25900 \cdot (0.805)^{10}$
Calculate $(0.805)^{10} \approx 0.115$
$V(10) \approx 25900 \cdot 0.115$

Answer:

$\$2979$