MATH SOLVE

6 months ago

Q:
# 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?

Accepted Solution

A:

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.

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.