Answer:
C. 3.8 years
Step-by-step explanation:
Exponential Growth
The natural growth of some magnitudes can be modeled by the equation:
[tex]P(t)=P_o(1+r)^t[/tex]
Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.
The actual population of deer in a forest is Po=800 individuals. It's been predicted the population will grow at a rate of 20% per year (r=0.2).
We have enough information to write the exponential model:
[tex]P(t)=800(1+0.2)^t[/tex]
[tex]P(t)=800(1.2)^t[/tex]
It's required to find the number of years required for the population of deers to double, that is, P = 2*Po = 1600. We need to solve for t:
[tex]800(1.2)^t=1600[/tex]
Dividing by 800:
[tex](1.2)^t=1600/800=2[/tex]
Taking logarithms:
[tex]t\log 1.2=\log 2[/tex]
Dividing by log 1.2:
[tex]t=\frac{\log 2}{ \log 1.2}[/tex]
Calculating:
t = 3.8 years
Answer: C. 3.8 years
