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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

Fish Farming A fish farmer has 5000 catfish in his pond. The number of catfish increases by 8 % per month, and the farmer harvests 300 catfish per month.

(a) Show that catfish population P n after n th months is given recursively by P 0 = 5000 and

P n = 1.08 P n 1 300

(b) How many fish are in the pond after 12 months?

To determine

a)

To prove:

The catfish population Pn after n months is given recursively by P0=10,000 and

Pn=1.08Pn1300.

Explanation

Given:

Farmer has 5000 catfish in his pond.

Catfish population increases by 8% per month and 300 catfish is harvested each month.

Approach:

Relate the population after n th months to the population after (n1) th months using the given information that population increases each month by 8% and 300 catfish is harvested.

Calculation:

Population after (n1) months is Pn1. Increment by 8% changes population to (1+08/100)Pn1=1.08Pn1

Harvesting 300 catfish we get the population after n months to be:

Pn=1

To determine

b)

To find:

The fish in the pond after 12 months.

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