Solve.
-There are currently 51 million cars in a certain country, increasing exponentially by 4.4% annually. How many years will it take for this country to have 60 million cars? Round to the nearest year.
A) 3 yr
B) 4 yr
C) 2 yr
D) 50 yr

Question

Quizplus · Accepted Answer

Let's use the formula for exponential growth:

A = P(1 + r)^t

Where: 
A = final amount (60 million cars) 
P = initial amount (51 million cars) 
r = annual growth rate (4.4% or 0.044 as a decimal) 
t = time (in years)

Plugging in the values, we get:

60,000,000 = 51,000,000(1 + 0.044)^t

Dividing both sides by 51,000,000:

1.1765 = 1.044^t

Using logarithms to solve for t:

log 1.1765 = log 1.044^t

t = log 1.1765 / log 1.044 ≈ 3.96

Rounding to the nearest year, we get 4 years. So it will take about 4 years for the country to have 60 million cars.

Solve. -There Are Currently 51 Million Cars in a Certain Country