Question

Nick bought a new car.
Each year the car depreciates in value by 12%.
Work out the number of years it takes for the car to half in value.

Answer 1

Using an exponential function, it is found that it takes 5.42 years for the car to halve in value.

What is an exponential function?

A decaying exponential function is modeled by:

$A(t) = A(0)(1 - r)^t$

In which:

• A(0) is the initial value.

• r is the decay rate, as a decimal.

In this problem, the car depreciates 12% a year in value, hence r = 0.12 and the equation is given by:

$A(t) = A(0)(0.88)^t$.

It halves in value at t years, for which A(t) = 0.5A(0), hence:

$A(t) = A(0)(0.88)^t$

$0.5A(0) = A(0)(0.88)^t$

$(0.88)^t = 0.5$

$\log{(0.88)^t} = \log{0.5}$

$t\log{0.88} = \log{0.5}$

$t = \frac{\log{0.5}}{\log{0.88}}$

t = 5.42.

It takes 5.42 years for the car to halve in value.

More can be learned about exponential functions at https://brainly.com/question/25537936

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