The population of a parish is growing with an annual percentage rate compounded continuously. The population reaches 1.1 times its previous size in 2 years. Find the annual percentage rate according to the exponential growth function. Write your answer in exact form, using ln (do not round).

The annual percentage rate according to the exponential growth function is 5%

An exponential growth is in the form:

y = abˣ;

where y, x are variables, a is the initial value of y and b > 1

Let y represent the population after x years.

Let us assume that initially the population is c. hence, a = c.

The population reaches 1.1 times its previous size in 2 years:

Hence the annual percentage rate = 1.05 - 1 = 5%

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Step-by-step explanation:

The population that grows with an annual percentage rate compounded continuously is given by:

The population reaches 1.1 times its previous size in 2 years.

This means that, when t=2,

We substitute to obtain:

This implies that:

Take natural log to get:

Therefore the annual percentage rate is

twenty-six miles over two gallons because the proportion for the original 13 miles to one gallon would be written 13/1 and, doing the same thing to the top and bottom, i multiplied by 2 and got 26/2