Question

Solve by using proper methods.

Answer 1

Answer:

Approximately after 66.15 years, there will be 100 coyotes left

Step-by-step explanation:

We can use the formula  $F=P(1+r)^t$ to solve this.

Where

F is the future amount (F=100 coyotes)

P is the initial amount (P=750 coyotes)

r is the rate of decrease per year (which is -3% per year or -0.03)

t is the time in years (which we need to find)

Putting all the information into the formula we solve.

Note: The logarithm formula we  will use over here is  $ln(a^b)=bln(a)$

So, we have:

$F=P(1+r)^t\\100=750(1-0.03)^t\\100=750(0.97)^t\\\frac{100}{750}=0.97^t\\\frac{2}{15}=0.97^t\\ln(\frac{2}{15})=ln(0.97^t)\\ln(\frac{2}{15})=tln(0.97)\\t=\frac{ln(\frac{2}{15})}{ln(0.97)}\\t=66.15$

Hence, after approximately 66.15 years, there will be 100 coyotes left.

Rounding, we will have 66 years