17. population growing at an annual rate r will triple in a time t given by the formula t = ln 3/r If the growth rate remains constant and equals 9% per year, how long will it take the population of the town to triple?

a. 6 . 6 years
b. 1 years
c. 5 . 3 years
d. 2 . 2 years
e. 12.2 years

E, 12.2 years

Given that the growth rate equals 9% per year, we can convert this percentage to a decimal form by dividing it by 100.

r = 9% = 0.09

To find how long it will take for the population to triple, we can use the formula:

t = ln(3) / r

Substituting the value of r:

t = ln(3) / 0.09

Using a calculator, we can find that ln(3) is approximately 1.0986.

t = 1.0986 / 0.09

Calculating this expression:

t ≈ 12.2

Therefore, it will take approximately 12.2 years for the population of the town to triple.

The correct option is e. 12.2 years.

To answer this question, we can use the given formula t = ln 3/r, where t represents the time it takes for the population to triple and r represents the annual growth rate.

First, let's calculate the value of r. The growth rate is given as 9% per year, which can be expressed as a decimal by dividing 9 by 100. Therefore, r = 0.09.

Next, substitute the values of r into the formula: t = ln 3/0.09.

To find the value of t, we can use a scientific calculator or an online natural logarithm calculator.

Approximating the value of ln 3/0.09, we find t ≈ 5.3 years.

Therefore, the correct answer is option c. 5.3 years.