a. Model the situation with an exponential function.
The exponential function that models the problem in this case is:
y = 1056 (1.28) ^ t
Where,
t: number of years
b. Find how many alligators there will be in 8 years.
For 8 years we must replace the value of t = 8 in the written equation.
We have then:
y = 1056 (1.28) ^ 8
y = 7609.28193
Nearest whole integer:
y = 7609
c. How many years will it take for the population to become 3000?
For this we should almost replace y = 3000 in the equation of part A.
We have then:
3000 = 1056 (1.28) ^ t
From here, we clear t:
(1.28) ^ t = (3000) / (1056)
We apply logarithm to both sides:
log1.28 ((1.28) ^ t) = log1.28 ((3000) / (1056))
t = log1.28 ((3000) / (1056))
t = 4.229619111 years.
