Write the word or phrase that best completes each statement or answers the question.
-In the formula $\mathrm { N } = \mathrm { Ie } \mathrm { kt } , \mathrm { N }$ is the number of items in terms of an initial population I at a given time $\mathrm { t }$ and $\mathrm { k }$ is a growth constant equal to the percent of growth per unit time. There are currently 68 million cars in a certain country, increasing by $1.2 \%$ annually. How many years will it take for this country to have 77 million cars? Round to the nearest year.
A) $10 \mathrm { yr }$
B) $183 \mathrm { yr }$
C) $5 \mathrm { yr }$
D) $8 \mathrm { yr }$

Question

Quizplus · Accepted Answer

The formula given is for exponential growth, $N = Ie^{kt}$. Here, $N = 77$ million, $I = 68$ million, and $k = 0.012$ (since 1.2% is 0.012 in decimal form). We need to solve for $t$. Rearranging the formula and solving for $t$ gives a value close to 10 years when rounded to the nearest year.

Write the Word or Phrase That Best Completes Each Statement N=Iekt,N\mathrm { N } = \mathrm { Ie } \mathrm { kt } , \mathrm { N }N=Iekt,N

Write the Word or Phrase That Best Completes Each Statement $\mathrm { N } = \mathrm { Ie } \mathrm { kt } , \mathrm { N }$