After a shipwreck, 120 rats manage to swim from the wreckage to a deserted island. The rat population on the island grows exponentially, and after 15 months, there are 280 rats on the island. A. Find a function that models the population t months after the arrival of the rats.
B. What will the population be 3 years after the shipwreck?
C. When will the population reach 2000 rats?

a.  

b.   Population after 3 years is 142

c.   50 years

Step-by-step explanation:

Given

Type of growth: Exponential

Initial number of rats = 120

Number of rats (15months) = 280

Solving (a)

Since the growth type is exponential, we make use of the following exponential progression

Where Xo is the initial population;

Xo = 125

is the current population at T month

So;

; when

Substitute these values in the above formula

Divide both sides by 120

Take 15th root of both sides

Subtract 1 from both sides

(Approximated)

Plug in values of R and Xo in

Write as a function

Hence, the function is

Solving (b):

Population after 3 years

In this case, T = 3

So:

(Approximated)

Solving (c): When population will reach 2000

Here: X(T) = 2000

So:

So:

Divide both sides by 120

Take Log of both sides

Apply law of logarithm

Divide both sides by Log(1.058)

Approximate

  the correct choice is marked

step-by-step explanation:

the first two graphs show multiple turning points. the last graphs matches the description in every detail.