13. In California’s gold rush, some towns grew exponentially. If a certain town started with 45 people and had 360 people 15 months later, what is the growth rate? (r can also be per month instead of per year)

Using the exponential function, the growth rate experienced during the California's gold rush is

The exponential function :

Substituting the values into the equation :

Divide both sides by 45

Take the In of both sides

Hence, the monthly growth rate is 13.86%

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The growth rate of the town is approximately 0.212 per month.

Explanation:

The exponential model is defined by the following formula:

(1)

Where:

- Initial population, dimensionless.

- Growth rate, measured in .

- Time, measured in months.

- Current population, dimensionless.

From (1), we clear the growth rate as follows:

(2)

If we know that , and , then the growth rate is:

The growth rate of the town is approximately 0.212 per month.

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to answer your question:

f(x)= a^x.  if x=0, f(x)=1  if x=1, f(x)=a  if x=1, f(x)=a^a