Multiple choice A B C or D?

For the first group we have the pairs:

year           population

0                20

1                 80

2                320

3                 1,280

4                 5,120

5                 20,480

Here we can see that the population quadruples each year

(4*20 = 80, 80*4 = 320, 320*4 = 1,280, etc...)

then the population equation is:

P(0) = 20

P(1) = 20*4

P(2) = (20*4)*4 = 20*4^2

We already can see the pattern, then we can write this relationship as:

P(t) = A*(4)^(t)

Where:

t represents time in years, and A is the initial population, that we know it is 20, then:

P(t) = 20*(4)^t

This is the function that represents the table.

B) Now we have a group of 20 squirrels and the population triples each year, with the same reasoning than before we can write the equation that models this situation as:

Q(t) = 20*(3)^t

C) Now, if the initial population of the second group is 40, the equation becomes:

Q(t) = 40*(3)^t

The population by year 3 is given by replacing t by 3, then:

Q(3) = 40*(3)^3 = 1080

And the population of the other group in year 3 is seen in the table, it is 1,280, then the population of the first group is bigger by year 3, and it is greater by:

1,280 - 1,080 = 200

So the first group is larger by 200 squirrels.