Suppose a car that sells for $40,000 depreciates 10% per year. How many years would it take for the car to have a value less than $25,000?

It would take 5 years for the car to have a value of less than $25,000

Step-by-step explanation:

Exponential Decaying Model

The exponential function is often used to model natural decaying processes, where the change is proportional to the actual quantity.

We have the initial value of a car is $40,000. Each year it depreciates by 10%.

Thus the first year its value is 90% of the initial value:

V1 = 90 * $40,000 / 100 = $36,000

By the second year its value is 90% of $36,000:

V2 = 90 * $36,000 / 100 = $32,400

Note the value for a year n is the original value multiplied by 90% (or 0.9) to the power of n:

To find the number of years needed to have a value of less than $25,000, we solve the equation:

Dividing by 40,000:

Taking logarithms:

n =4.5

We'll round up to n = 5

It would take 5 years for the car to have a value of less than $25,000

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2