Question

A new car sells for $30,000. The value of the car decreases by 16% annually. After how many years will the car be worth less than $10,000.
a. after 2 years

b. after 6 years

c. after 8 years

d. not enough information

(answer c is incorrect)

Answer 1

Answer: after 6 years.

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^t

Where

A represents the value of the car after t years.

t represents the number of years.

P represents the initial value of the car.

r represents rate at which the value is decreasing.

From the information given,

P = 3000

A = < 10000

r = 16% = 16/100 = 0.16

Therefore

10000 = 30000(1 - 0.16)^ t

1000/30000 = (0.84)^t

0.333 = (0.84)^t

Taking log of both sides to base 10

Log 0.333 = log0.84^t = tlog0.84

- 0.4772 = t × - 0.0757

t = - 0.4772/ - 0.0757 = 6.3 years