Answer: 10.4 years
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