The population of a town can be modeled using the formula P=25000e^0.03t

Question

, where t is the number of years after 2012
and P is the town's population. Which of the following equations can be used to find the number of years after 2012
that the population will double to 50000
?

Answer 1

To find the number of years after 2012 (t) when the population will double from 25,000 to 50,000, you can set up the equation based on the given population model.

The population formula is:

\[ P = 25000 e^{0.03t} \]

You want to find t when P = 50,000. So you can set up the equation:

\[ 50000 = 25000 e^{0.03t} \]

Now, to solve for t, you can simplify and rearrange the equation:

1. Divide both sides by 25,000:

\[ 2 = e^{0.03t} \]

2. Take the natural logarithm (ln) of both sides:

\[ \ln(2) = \ln(e^{0.03t}) \]

3. Use the property of logarithms that allows you to bring down the exponent:

\[ \ln(2) = 0.03t \]

4. Finally, solve for t:

\[ t = \frac{\ln(2)}{0.03} \]

Thus, the equation you would use to find the number of years after 2012 when the population will double is:

\[ t = \frac{\ln(2)}{0.03} \]