Solve by using proper methods.Let's say that we had a 750 coyotes that were decreasing at a rate of 3% per year. How many years would it be until we had only 100 coyotes left? Show your work.

Answer:Approximately after 66.15 years, there will be 100 coyotes leftStep-by-step explanation:We can use the formula  [tex]F=P(1+r)^t[/tex] to solve this.WhereF 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  [tex]ln(a^b)=bln(a)[/tex]So, we have:[tex]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[/tex]Hence, after approximately 66.15 years, there will be 100 coyotes left.Rounding, we will have 66 years