Apopulation of 550 rabbits is increasing by 2.5% each year the function y = 5.5 (1.025)× give the population of rabbits in hundreds x year from now about how long will it take the population to reach 600 rabbits? 1200 rabbits?

Given function : y = 5.5 (1.025)×, Where exponent x is number of years from now and y give the population of rabbits in hundreds.

We need to find the time(s) when there will be 600 rabbits and 1200 rabbits.

Solution: We know, y represents the population of rabbits in hundreds.

a) Plugging y=600 in given function, we get

600 = 5.5 (1.025)×

Dividing both sides by 5.5

600/5.5 = 5.5 (1.025)× / 5.5

600/5.5 = (1.025)×

Taking natrual log on both sides, we get

ln (600/5.5) = ln (1.025)×

ln (600/5.5) = x ln (1.025)

Dividing both sides by ln(1.05), we get

x= 96.171 years apprimately.

b) Plugging y=1200 in given function, we get

1200 = 5.5 (1.025)×

Dividing both sides by 5.5

1200/5.5 = 5.5 (1.025)× / 5.5

1200/5.5 = (1.025)×

Taking natrual log on both sides, we get

ln (1200/5.5) = ln (1.025)×

ln (1200/5.5) = x ln (1.025)

Dividing both sides by ln(1.05), we get

x= 110.377 years apprximately.

Therefore, it will take 96.171 years apprimately to population to reach 600 rabbits and 110.377 years approximately to population to reach 1200 rabbits.

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