Question

I need help ASAP! I took a screenshot of the question and linked it.

Answer 1

Before we solve this problem:

    ⇒ let's figure out what all the variables in the equation stand for

• t: number of years after initial rabbit population
• r(t): number rabbits in 't' years

Question 16: How many rabbits will there be in 8 years?

• Since it is asking how many rabbits there be in 8 years

         ⇒ that means we substitute 8 into 't' of the equation

                 $R(t) = 225e^{0.375t} =225e^{0.375*8} =225e^3 = 4519.2$

          *we will round down the number of rabbits since it is impossible to

           have 0.2 of a rabbit

       There will be 4519 rabbits in 8 years.

Question 17: When will the population be 15000?

• Since it asking for when the population or R(t) will be 15000

         ⇒ we substitute 15000 into 'R(t)' of the function and solve for 't'

                $R(t) = 225e^{0.375t}\\15000=225*e^{0.375t}\\\frac{15000}{225} =e^{0.375t}\\ln(\frac{15000}{225})=0.375t\\ t = 11.2$

            *in this case, you want it to the nearest year, round it up since we

             asked for how many years, and if we were to say 11, the

            the population of rabbits wouldn't have reached that number yet,

           so we will round up to ensure that number has been reached by

           that year.

       

       It will take at least 12 years for the rabbit population to reach 15000

Hope that helps!