Question

There are currently 73 million cars in a certain country, decreasing by 1.7% annually.

Answer 1

Answer:

17.6 years

Step-by-step explanation:

There are currently 73 million cars in a certain country, decreasing by 1.7% annually.

How many years will it take for this country to have 54 million cars? Round to the

nearest year.

We use the formula

y = a(1 - r)^t

a = Initial amount = 73 million cars

y = Future amount = 54 million cars

r = decreasing rate = 1.7 % = 0.017

t = time is unknown

54,000,000 = 73,000,000(1 - 0.017)^t

Divide both sides by 73,000,000

54,000,000/73,000,000 = (0.983)^t

0.7397260274 = (0.983)^t

Take the logarithm of both sides

log 0.7397260274 = Log (0.983)^t

log 0.7397260274 =t log (0.983)

t = log 0.7397260274/log 0.983

t = -0.13092910029/-0.00744648216

t = 17.5826783005 years

Approximately = t = 17.6 years