The function $Y(x)=45.21 \ln \frac{x}{3.5}$ can be used to estimate the number of years $Y(x)$ after 1980 required for a certain country's population to reach $\mathrm{x}$ million people. In what year will the country's population reach 14 million?
A) About 2043
B) About 2033
C) About 2053
D) About 2048

Question

Quizplus · Accepted Answer

To find the year when the population reaches 14 million, substitute $x = 14$ into the given function: $Y(14) = 45.21 \ln \frac{14}{3.5}$. Simplifying inside the logarithm gives $\ln 4$, and calculating $45.21 \ln 4$ gives approximately 63 years after 1980. Adding 63 to 1980 gives 2043.

The Function Y(x)=45.21ln⁡x3.5Y(x)=45.21 \ln \frac{x}{3.5}Y(x)=45.21ln3.5x​ Can Be Used to Estimate the Number of Years

The Function $Y(x)=45.21 \ln \frac{x}{3.5}$ Can Be Used to Estimate the Number of Years