Question

3. Consider a population that has an initial population of 100 and grows according to the recursive rule: Pn = Pn-1 + 35. What will be the population after 50 years?

Answer 1

The population after 50 years will be 1850.

Explanation:

We are given the following in the question:

`P_n =P_(n-1) + 35`

which is the recursive rule for a population.

Initial population = 100

`P_0 = 100`

The explicit form of given recursive relation can be written as:

`P_n = 100 + 35n`

We have to find the population after 50 years.

We put n = 50 in the explicit form.

`P_(50) = 100 + 35(50) = 1850`

Thus, the population after 50 years will be 1850.