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 57 million cars in a certain country, decreasing by $2.2 \%$ annually. How many years will it take for this country to have 30 million cars? Round to the nearest year.
A) $3 \mathrm { yr }$
B) $12 \mathrm { yr }$
C) $150 \mathrm { yr }$
D) $29 \mathrm { yr }$

Question

Quizplus · Accepted Answer

Given the formula $N = Ie^{kt}$, where $N$ is the final amount, $I$ is the initial amount, $k$ is the rate of growth (in this case, a negative value because it's a decrease), and $t$ is the time in years. We are given $I = 57$ million cars, $N = 30$ million cars, and $k = -0.022$ (since a decrease of $2.2\%$ is $-2.2\%$ or $-0.022$ in decimal form). We need to solve for $t$. Rearranging the formula and solving for $t$ involves logarithms. Plugging the values into the formula and solving for $t$ will give a value close to $29$ years, hence option D is correct.

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 $\mathrm { N } = \mathrm { Ie } \mathrm { kt } , \mathrm { N }$