A population grow according to an exponential growth model, with P0=40 and P1=44 Complete the recursive formula Pn=40•Pn-1 Write the explicit formula for Pn

Answer 1

To find the explicit formula for Pn, we can use the formula:

Pn = P0 * (1 + r)^n

where r is the growth rate.

We can find the growth rate by using the information given:

P1 = P0 * (1 + r)

44 = 40 * (1 + r)

1 + r = 44/40 = 1.1

r = 0.1

Now we can substitute P0 = 40 and r = 0.1 into the formula to get:

Pn = 40 * (1 + 0.1)^n

Simplifying:

Pn = 40 * 1.1^n

Therefore, the explicit formula for Pn is Pn = 40 * 1.1^n.