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
2 years ago
1 year ago
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.
1 year ago
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.