a population is growing continuously at a rate of 3%. if the population is now 5 million, when will the…

Explanation:

Step1: Identify the continuous - growth formula

The formula for continuous population growth is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the growth rate, and $t$ is the time. Here, $P = 5$ (in millions), $r=0.03$, and $A = 8.3$ (in millions).

Step2: Substitute the values into the formula

Substitute the values into $A = Pe^{rt}$: $8.3=5e^{0.03t}$.

Step3: Solve for $t$

First, divide both sides by 5: $\frac{8.3}{5}=e^{0.03t}$, so $1.66 = e^{0.03t}$. Then, take the natural - logarithm of both sides: $\ln(1.66)=\ln(e^{0.03t})$. Since $\ln(e^{x}) = x$, we have $\ln(1.66)=0.03t$. Finally, solve for $t$: $t=\frac{\ln(1.66)}{0.03}$. We know that $\ln(1.66)\approx0.5068$, so $t=\frac{0.5068}{0.03}\approx16.89$.

Answer:

Approximately $16.89$ years.