A population of deer increases at a rate of 4% annually. If the starting population is 800 deer, how long will it take for the population to grow to 1,200? Round your answer to the nearest tenth of a year.

10.4 years

Step-by-step explanation:

A deer population grows at a rate of 4% annually. The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

y = b(1 + r)^ t

Where

y represents the population after t years.

t represents the number of years.

b represents the initial population.

r represents rate of growth.

From the information given,

b = 800

r = 4% = 4/100 = 0.04

y = 1200

Therefore

1200 = 800(1 + 0.04)^t

1200/800 = (1.04)^t

1.5 = (1.04)^t

Taking log of both sides to base 10

Log 1.5 = log1.04^t = tlog1.04

0.1761 = t × 0.017

t = 0.1761/0.017

t = 10.4 years