Car Depreciation Model

00:00 6 marks

The value of a car depreciates each year. The value, $V$ dollars, of the car $n$ years after it was purchased is modelled by the geometric sequence $V_n = 25000 \times (0.88)^n$.

(a) Write down the purchase price of the car. [1]
(b) Find the value of the car after 4 years. [2]
(c) Calculate the number of years it takes for the car’s value to fall below $$10000$. [3]

Part a

2 minutes 1 marks

Question

Write down the purchase price of the car. [1]

Hint Hint

Hint

Remember, any number raised to the power of 0 is 1. Substitute $n = 0$ into $V_n = 25000 \times (0.88)^n$.

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Complete Answer

$25000$ dollars

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Part b

3 minutes 2 marks

Question

Find the value of the car after 4 years. [2]

Hint Hint

Hint

Substitute $n = 4$ into the model $V_n = 25000 \times (0.88)^n$ and then round your answer correctly.

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Complete Answer

Approximately $14990$ dollars

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Part c

5 minutes 3 marks

Question

Calculate the number of years it takes for the car’s value to fall below $$10000$. [3]

Hint Hint

Hint

Set up the inequality $25000(0.88)^n < 10000$ and solve for $n$ using logarithms.

Answer Answer
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Complete Answer

8 years

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