Question

The value of a motorbike is $12400. Each year, the value of the motorbike decreases exponentially by 15%. Calculate the value of the motorbike after 3 years.

a) $6500
b) $7050
c) $7597.50
d) $8127.87

Answer 1

To calculate the value of a motorbike after 3 years with an annual exponential decay of 15%, apply the formula V = P(1 - r)^t. Plugging in the initial value of $12,400 and decay rate of 0.15, the result is approximately $7,597.50.

Step-by-step explanation:

The question asks us to calculate the value of a motorbike after 3 years, given that its value decreases exponentially by 15% each year from an initial value of $12,400. This is a mathematics question that deals with exponential decay.

To find the value after 3 years, we need to apply the formula for exponential decay:

V = P(1 - r)^t

Where:

• V is the final value of the motorbike after time t
• P is the initial value of the motorbike
• r is the rate of decay (expressed as a decimal)
• t is the time in years

Substituting the given values, we have:

V = 12,400(1 - 0.15)^3

Simplifying further:

V = 12,400(0.85)^3

V = 12,400(0.614125)

V ≈ $7,597.50

So the value of the motorbike after 3 years is $7,597.50, which corresponds to option (c).