If a population of 9 million begins to increase at a rate of 0.33% each month, in how many months will it be 14 million? Round your answer to two decimal places.
A)160.89 months
B)201.05 months
C)134.11 months
D)174.28 months
E)67.17 months

Question

If a population of 9 million begins to increase at a rate of 0.33% each month, in how many months will it be 14 million? Round your answer to two decimal places. ​
A)160.89 months
B)201.05 months
C)134.11 months
D)174.28 months
E)67.17 months

Quizplus · Accepted Answer

We can use the formula for exponential growth: A = P(1+r)^t, where A is the final amount, P is the initial amount, r is the growth rate as a decimal, and t is the time in months.

Plugging in the given values, we get:

14,000,000 = 9,000,000(1+0.0033)^t

Divide both sides by 9,000,000:

1.55556... = (1+0.0033)^t

Take the natural log of both sides:

ln(1.55556...) = ln(1+0.0033)t

Divide both sides by ln(1+0.0033):

t = ln(1.55556...)/ln(1+0.0033)

Using a calculator, we get t ≈ 134.11 months.

Therefore, the answer is C: 134.11 months.

If a Population of 9 Million Begins to Increase at a Rate