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Expert-verified Found in: Page 810 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # A pond currently has 2000 trout in it. A fish hatchery decides to add an additional 20 trout each month. In addition, it is known that the trout population is growing 3% per month. The size of the population after n months is given by the recursively defined sequence.${p}_{0}=2000;{p}_{n}=1.03{p}_{n-1}+20$(a) How many trout are in the pond at the end of the second month? That is, what is p2?(b) Using a graphing utility, determine how long it will bebefore the trout population reaches 5000.

(a) The number of trout in second month, p2 is 2162.

(b) The population after 26 months will be 5084.2433.

See the step by step solution

## Step 1. Write the given information.

The current population:

${p}_{0}=2000$

& Size of population after n months can be defined as:

${p}_{n}=1.03{p}_{n-1}+20$

## Step 2. Use the population size formula as given.

Using the recursively defined formula for p2 :

${p}_{1}=1.03{p}_{1-1}+20\phantom{\rule{0ex}{0ex}}⇒{p}_{1}=1.03\left(2000\right)+20\phantom{\rule{0ex}{0ex}}⇒{p}_{1}=2080\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}{p}_{2}=1.03{p}_{2-1}+20\phantom{\rule{0ex}{0ex}}⇒{p}_{2}=1.03\left(2080\right)+20\phantom{\rule{0ex}{0ex}}⇒{p}_{2}=2162.4\phantom{\rule{0ex}{0ex}}$

## Step 3. Use the given formula for calculating the size of population after 26 months.

Using graphing calculator to compute the population size up to 26 months.  ### Want to see more solutions like these? 