A town has a population of 13000 and grows at 4.5% every year. To the nearest tenth of a year, how long will it be until the population will reach 16900?

it will take 6 years until the population will reach 16900

Step-by-step explanation:

The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

A = P(1 + r)^ t

Where

A represents the population after t years.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

A = 16900

P = 13000

r = 4.5% = 4.5/100 = 0.045

Therefore

16900 = 13000(1 + 0.045)^t

16900/13000 = (1.045)^t

1.3 = (1.045)^t

Taking log of both sides to base 10

Log 1.3 = log1.045^t = tlog1.045

0.114 = 0.0191t

t = 0.114/0.0191

t = 6.0 years to the nearest tenth

the answer is 21%.