Question

A population grows according to an exponential growth model, with P 0 = 50 and P 1 = 65 Complete the recursive formula: P n = × P n − 1

Answer 1

The recursive formula for the exponential growth model given the initial population P0=50 and P1=65 is Pn = 1.3 × Pn-1.

Step-by-step explanation:

The student is asking about an exponential growth model for population, which describes how a population size changes over time. We know the initial population size, P0, is 50, and the size after one time period, P1, is 65. To complete the recursive formula Pn = … × Pn-1, we need to find the growth factor that shows how much the population multiplies by each time period.

To find this growth factor, we divide P1 by P0:

growth factor = P1 / P0
= 65 / 50
= 1.3

Therefore, the recursive formula for the population growth is
Pn = 1.3 × Pn-1.