Question

Jackson purchases a new car for $48,000. The car’s value can be modeled by the following exponential function:y=48000(0.76)^t where y represents the cars value and t represents time in years . What is the decay rate expressed as a percentage?

Answer 1

The decay rate expressed as a percentage is of 24%.

Explanation:

The equation for the value of the car has the following format:

`y(t) = y0(1-r)^(t)`

In which y(t) is the value of the car after t years, y0 is the initial value and r is the decay rate, as a decimal.

In this problem:

y=48000(0.76)^t

So

Comparing to the general formula:

1 - r = 0.76

r = 1 - 0.76

r = 0.24

To convert from decimal to percentage, we multiply by 100

The decay rate expressed as a percentage is of 24%.