Question

An animal reserve has 40000 elk if the population is increasing at a rate of 19% per year how long will it take for the population to reach 80000 if necessary round your answer to the nearest tenth

Answer 1

Answer:

Step-by-step explanation:

This is of the form

$P(t)=a(b)^t$

Where P(t) is the ending population, a is the original population, b is the growth rate, and t is time in years.  We have everything we need to solve for t.  

$80000=40000(1.19)^t$

Let me explain the growth rate quickly.  If the exponential function is a growth function, that means (in this particular situation) that we have 100% of the population and we are increasing it by 19%.  That makes the growth rate 119%, which in decimal form is 1.19.  

Begin by dividing both sides by 40000 to get

$2=(1.19)^t$

To get that t out of its current exponential position, take the natural log of both sides:

$ln(2)=ln(1.19)^t$

and the rules of logs say we can bring the exponent down out front:

ln(2) = t*ln(1.19)

Divide both sides by ln(1.19) to get t alone:

$\frac{ln(2)}{ln(1.19)}=t$

Doing that calculation on your calculator gives you that

t = 3.9846...

but rounding to the nearest tenth gives you that

t = 4.0 years