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 $\mathrm { I }$ at a given time $\mathrm { t }$ and $\mathrm { k }$ is a growth constant equal to the percent of growth per unit time. How long will it take for the population of a certain country to double if its annual growth rate is $7.5 \%$ ? Round to the nearest year.
A) $4 \mathrm { yr }$
B) $9 \mathrm { yr }$
C) $27 \mathrm { yr }$
D) $1 \mathrm { yr }$

Question

Quizplus · Accepted Answer

To find the time it takes for the population to double, we set $N = 2I$ (since doubling means the final population is twice the initial population), and substitute $k = 0.075$ (since a 7.5% growth rate means $k = 7.5/100 = 0.075$). The equation becomes $2I = Ie^{0.075t}$. Dividing both sides by $I$ and taking the natural logarithm of both sides gives $\ln(2) = 0.075t$. Solving for $t$ gives $t = \ln(2)/0.075$, which approximately equals 9 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 $\mathrm { N } = \mathrm { Ie } \mathrm { kt } , \mathrm { N }$