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PROBLEM 6 A lake initially contains 1000 fish. Suppose that in the absence of predators or other causes of removal, the fish population increases by 10% cach month. However, factoring in all causes, 80 fish are lost each month. Give a recurrence relation for the population of fish after n months. How many fish are there after 5 months? If your fish model predicts a non-integer number of fish, round down to the next lower integer.

PROBLEM 6 A lake initially contains 1000 fish. Suppose that in the absence of predators or other causes of removal, the fish population increases by 10% cach month. However, factoring in all causes, 80 fish are lost each month. Give a recurrence relation for the population of fish after n months. How many fish are there after 5 months? If your fish model predicts a non-integer number of fish, round down to the next lower integer.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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PROBLEM 6 A lake initially contains 1000 fish. Suppose that in the absence of predators or other causes of removal, the fish population increases by 10% cach month. However, factoring in all causes, 80 fish are lost cach month. Give a recurrence relation for the population of fish after n months. How many fish are there after 5 months? If your fish model predicts a non-integer number of fish, round down to the next lower integer.
Transcribed Image Text:PROBLEM 6 A lake initially contains 1000 fish. Suppose that in the absence of predators or other causes of removal, the fish population increases by 10% cach month. However, factoring in all causes, 80 fish are lost cach month. Give a recurrence relation for the population of fish after n months. How many fish are there after 5 months? If your fish model predicts a non-integer number of fish, round down to the next lower integer.
Expert Solution
Step 1

Given data:

  • Number of fishes initially=1000
  • Increase in percentage of population every month=10%
  • Fishes lost each month=80

Using the given data, the number of fishes each month can be written as:

Months 1 2 3 4 5 6
Fishes 1000 1020 1042 1066 1093 1122

Finding the recurrence relation using Binary Search Algorithm,

BSa,i,j,x

Here, i=1000 and j=1122

Mid value=i+j2=21222=1061

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