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You are buying a used car which costs $12,000. You plan to sell the car after keeping it for 5 years. Research shows that this car will lose value at a rate of 8% per year. How much will tbe car be worth after 5 years?

Answer :

ProfessorAlvarez

[tex]\text{Use the formula:}\,A=P(1-r)^t\\\\\text{Plug your values into the equation}\\\\A=12,000(1-0.08)^5\\\\\text{Solve:}\\\\12,000(1-0.08)^5\\\\12,000(0.92)^5\\\\12,000(0.659)\\\\\boxed{\$7,908.98}[/tex]

raphealnwobi

The car would be worth $7909 after 5 years.

Since the car will lose value at a rate of 8% per year this is an exponential decay. An exponential decay is in the form:

y = abˣ;

where y, x are variables, a is the initial value of y and b < 1

Let y represent the worth of the car after x years.

Since the car cost $12000, hence a = 12000, also the car will lose value at a rate of 8% per year. hence:

b = 100% - 8% = 0.92

Therefore:

y = 12000(0.92)ˣ

After 5 years:

y = 12000(0.92)⁵ = $7909

Therefore the car would be worth $7909 after 5 years.

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