Choose the one alternative that best completes the statement or answers the question.
-In the formula N $\mathrm { N } = \mathrm { Ie } ^ { \mathrm { kt } }$ N is the number of items in terms of an initial population I at a given time and k is a growth constant equal to the percent of growth per unit time. There are currently 59
Million cars in a certain country, increasing by 1.2% annually. How many years will it take for this
Country to have 78 million cars? Round to the nearest year.
A) 5 yr
B) 16 yr
C) 245 yr
D) 23 yr

Question

Quizplus · Accepted Answer

Using the formula $ N = Ie^{kt} $, where $ N = 78 $ million, $ I = 59 $ million, and $ k = 0.012 $, solve for $ t $:  $ 78 = 59e^{0.012t} $  $ \frac{78}{59} = e^{0.012t} $  Taking the natural logarithm of both sides:  $ \ln(\frac{78}{59}) = 0.012t $  $ t = \frac{\ln(\frac{78}{59})}{0.012} \approx 23 $ years.

Choose the One Alternative That Best Completes the Statement or Answers