Question

Kaylen bought a new motorcycle for $5, 800. After 4 years, the bike is worth $4,926.21.

If Kaylen assumes the value of the motorcycle depreciates according to an exponential decay function, with t = 0 corresponding to the purchase date,
the decay rate is what percentage per year.

Answer 1

We can use the formula for exponential decay:

V = V0e^(-kt)

where:

V0 = initial value

V = value after time t

k = decay rate

t = time

We can use the information given to find k. We know that the initial value is $5,800, and the value after 4 years is $4,926.21. So we have:

V0 = 5800

V = 4926.21

t = 4

Substituting into the formula, we get:

4926.21 = 5800e^(-4k)

Dividing both sides by 5800, we get:

0.849355 = e^(-4k)

Taking the natural logarithm of both sides, we get:

ln(0.849355) = -4k

Solving for k, we get:

k = -ln(0.849355)/4 ≈ 0.0327

So the decay rate is approximately 0.0327 per year, or 3.27% per year