Question

A population grows according to an exponential growth model, with P0 = 20 and P1 = 25. Complete the recursive formula: Pn = ___*Pn-1

a) Pn = Pn-1 + 5
b) Pn = Pn-1 - 5
c) Pn = Pn-1 * 5
d) Pn = Pn-1 / 5

Answer 1

The closest option for the recursive formula reflecting the exponential growth model for a population that grows from 20 to 25 is Pn = Pn-1 * 5, although the exact factor should be 1.25 and not 5.

Step-by-step explanation:

The question deals with a population following an exponential growth model. To complete the recursive formula for the given population growth, we need to find the growth factor between P0 and P1. Since P0 = 20 and P1 = 25, the population grows by a factor of 25/20, which simplifies to 1.25. Therefore, the recursive formula that reflects this exponential growth is Pn = 1.25 * Pn-1. Among the options provided, none matches exactly since this is not a constant increase of 5, decrease of 5, or multiplication by 5. If the problem expects an answer from the given options, there is a mistake, and none of the choices are correct. However, if we are to ascertain the pattern, the closest choice would be option c) Pn = Pn-1 * 5, which represents a form of exponential growth, although the factor of 5 is not correct according to the values given.