High School

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You buy a used car for $20,000. It depreciates at the rate of 21% per year. Find the value of the car after 5 years. Write the exponential decay function and solve, showing your work.

a. Exponential decay function: [tex]V(t) = 20000 \times (0.79)^t[/tex]

b. [tex]V(5) = 20000 \times (0.79)^5 \approx \$8,031.05[/tex]

c. Exponential decay function: [tex]V(t) = 20000 \times (0.21)^t[/tex]

d. [tex]V(5) = 20000 \times (0.21)^5 \approx \$352.36[/tex]

Answer :

Final answer:

The value of the car after 5 years is approximately $8,031.05.

Explanation:

To find the value of the car after 5 years, we can use the exponential decay function: V(t) = 20000 * (0.79)^t. In this function, V(t) represents the value of the car after t years. We substitute t=5 into the equation to find the value after 5 years:

V(5) = 20000 * (0.79)^5 ≈ $8,031.05

Therefore, the value of the car after 5 years is approximately $8,031.05.

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