Question

The population of deer forest is currently 800 individuals. Scientists predict that this population will grow at a rate of 20 percent per year.

Answer 1

Answer:

C. 3.8 years

Step-by-step explanation:

Exponential Growth

The natural growth of some magnitudes can be modeled by the equation:

$P(t)=P_o(1+r)^t$

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:

$P(t)=800(1+0.2)^t$

$P(t)=800(1.2)^t$

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:

$800(1.2)^t=1600$

Dividing by 800:

$(1.2)^t=1600/800=2$

Taking logarithms:

$t\log 1.2=\log 2$

Dividing by log 1.2:

$t=\frac{\log 2}{ \log 1.2}$

Calculating:

t = 3.8 years

Answer: C. 3.8 years