Chapter 8, Problem 32CR

To determine

Find the recursive rule for the population of the town.

Answer to Problem 32CR

The recursive rule for the given population is $p_n=\left(0.04\right)p_{n-1}$ .

Explanation of Solution

Given:

The population of town $\left(11,120\right)$ is increases at a rate of about $4\%$ .

Calculation:

For the given data, geometric sequence is

  $p_1=11120{\left(0.04\right)}^{1-1}$

  $r=0.04$

The recursive equation for the geometric series is $a_n=r{a}_{n-1}$ .

Substitute the value of $r=0.04$ in the recursive equation.

  $p_n=\left(0.04\right)p_{n-1}$

Hence the recursive rule for the given population is $p_n=\left(0.04\right)p_{n-1}$ .