Question

Question 1A population grows according to an exponential growth model. The initial population is Po = 4, and thegrowth rate is r = 0.35.Then:P1 =P2 =Find an explicit formula for Pr. Your formula should involve n.Pn =Use your formula to find PuiP11 =Give all answers accurate to at least one decimal place

Answer 1

We know the initial population is 4

The growth rate is .35

P1 = P0 + P0*.35 = P0(1+.35)

P1 = 4 + 4(.35) = 4( 1+.35) = 4(1.35) = 5.4

P2 = P1 + P1* .35 = P1 ( 1+.35) =

5.4( 1.35) =7.29

Notice that we are multiplying the previous term by 1.35 each time

We can rewrite P2

P2 = P1 ( 1.35) =

Replacing P1 with P0(1.35)

P2 = P0(1.35) ( 1.35)

P2 = P0 ( 1.35) ^2

The general formula is

Pn = P0 ( 1.35) ^n

P11 = P0 (1.35) ^11

= 4 ( 1.35) ^11

= 108.5754017