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erma4kov [3.2K]
3 years ago
15

In 2012 your car was worth $10,000. In 2014 your car was worth $8,850. Suppose the value of your car decreased at a constant rat

e of change. Define a function f to determine the value of your car (in dollars) in terms of the number of years t since 2012.
Mathematics
1 answer:
monitta3 years ago
7 0

Answer:

The function to determine the value of your car (in dollars) in terms of the number of years t since 2012 is:

f(t) = 10000(0.9407)^t

Step-by-step explanation:

Value of the car:

Constant rate of change, so the value of the car in t years after 2012 is given by:

f(t) = f(0)(1-r)^t

In which f(0) is the initial value and r is the decay rate, as a decimal.

In 2012 your car was worth $10,000.

This means that f(0) = 10000, thus:

f(t) = 10000(1-r)^t

2014 your car was worth $8,850.

2014 - 2012 = 2, so:

f(2) = 8850

We use this to find 1 - r.

f(t) = 10000(1-r)^t

8850 = 10000(1-r)^2

(1-r)^2 = \frac{8850}{10000}

(1-r)^2 = 0.885

\sqrt{(1-r)^2} = \sqrt{0.885}

1 - r = 0.9407

Thus

f(t) = 10000(1-r)^t

f(t) = 10000(0.9407)^t

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