There are currently 71 million cars in a certain country dec

There are currently 71 million cars in a certain country, decreasing by 1.5% annually. How many years will it take for this country to have 42 million cars? Round to the nearest year.

Solution

Po = 71 million

rate = 1.5%

So, equation can be given as : P(t) = Po (1-r)^t

= 71(1 - 0.015)^t

P(t) = 71(0.985)^t

Now P(t) = 42 ; find t:

42 = 71(0.985)^t

take natural log on both sides:

0.5915 = (0.985)^t

ln(0.5915) = t*ln(0.985)

t = 34.73 = 35 years