After a shipwreck, 120 rats manage to swim from the wreckage to a deserted island. The population on the island grows exponentially according to the model n(t)-ne", where n(t)is the number of rats at time t in months. 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? Round to a whole number. c. When will the population reach 2000 rats?

Complete Question

The  complete question is shown on the first uploaded image  

a

b

c

Step-by-step explanation:

From the question we are told that

    The  original number of  rats that swim from the wreckage to a deserted island is

   The population on the island grows exponentially according to the model

     The  number of rats after t =  15 months is  280

So

=>  

=>  

=>  

=>  

Therefore the population t months after the arrival of the rats is mathematically represented as

Here t is in months

Considering question b

   For  t =  3 years  =  12 * 3 =  36 months

   Then the number of rats that will be present is mathematically represented as

Considering question c

Now  the number of rats considered is  n(t) =  2000

So  

=>    

=>  

Taking natural log of both sides

=>  

=>  

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction