Solve.
-Use the formula $\mathrm{N}=\mathrm{Ie}$, $\mathrm{kt}$, where $\mathrm{N}$ is the number of items at time $\mathrm{t}$, $\mathrm{I}$ is the initial amount, and $\mathrm{k}$ is a growth constant equal to the percent of growth (expressed in decimal form) per unit of time. There are currently 56 million cars in a certain country, increasing by $4.1 \%$ annually. How many years will it take for this country to have 78 million cars? Round to the nearest year.
A) $4 \mathrm{yr}$
B) $75 \mathrm{yr}$
C) $5 \mathrm{yr}$
D) $8 \mathrm{yr}$

Question

Quizplus · Accepted Answer

To solve for the number of years ($t$), we use the given formula $N = Ie^{kt}$ with $N = 78$ million, $I = 56$ million, and $k = 0.041$ (since 4.1% expressed as a decimal is 0.041). Rearranging the formula to solve for $t$, we get $t = \frac{\ln(N/I)}{k}$. Substituting the given values, $t = \frac{\ln(78/56)}{0.041}$, which when calculated gives a value close to 8 years.

Solve -Use the Formula N=Ie\mathrm{N}=\mathrm{Ie}N=Ie kt\mathrm{kt}kt , Where N\mathrm{N}N Is the Number of Items at Time

Solve
-Use the Formula $\mathrm{N}=\mathrm{Ie}$ $\mathrm{kt}$ , Where $\mathrm{N}$ Is the Number of Items at Time