Question

A town with a population of 600 is expected to grow at an annual rate of 5%. Write an equation and find the number of years it is expected to take the town to reach a population of 900.

Answer 1

Answer:

t = 8.31 years

Step-by-step explanation:

This is compound growth with a growth rate of 5%, initial count of 600 and final count of 900.

The appropriate equation is P  = Po (1 + 0.05)^t, where t represents the number of years required for the population to reach P:

900 = 600 (1.05)^t.  Let's solve this for t:

Dividing both sides by 600, we get 900/600 = 1.05^5, or

1.5 = 1.05^t.

To solve for t, take the log of both sides:

ln 1.5 = t*ln 1.05, or

t = (ln 1.5) / (ln 1.05)

This evaluates to t = 8.31 years.