The snake population in a swamp Is 1056. The population of the snakes is increasing by a factor of 28% each year.

a. Model the situation with an exponential function.

b. Find how many alligators there will be in 8 years.

c. How many years will it take for the population to become 3000?

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.