A population starts with 16 carpet beetles and in a week the population increase by 1 new beetle for every 4 beetles that were there the previous week which can be shown in the following table: Week 0 Week 1 Week 2 Week 3 Week 5 = 49 Week 4 16 20 25 = 31 = 39 How many beetles do you estimate there will be by Week 8?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A population starts with 16 carpet beetles and in a week the population increase by 1
new beetle for every 4 beetles that were there the previous week which can be shown
in the following table:
Week 0 Week 1 Week 2 Week 3
= 31
Week 5
= 49
Week 4
16
20
25
= 39
How many beetles do you estimate there will be by Week 8?
Transcribed Image Text:A population starts with 16 carpet beetles and in a week the population increase by 1 new beetle for every 4 beetles that were there the previous week which can be shown in the following table: Week 0 Week 1 Week 2 Week 3 = 31 Week 5 = 49 Week 4 16 20 25 = 39 How many beetles do you estimate there will be by Week 8?
Expert Solution
Step 1

given data is

Week 0 week 1 week 2 week 3 week 4 week 5
16 20 25 31 39 49

according to question population increased by 1 new beetles for every 4 beetles that were there the previous week.

now we will check a formula

                  Wn+1-Wn=WnR10020-16=16R11004=4R125R1=25%                                              25-20=20R2100,5=R25,R2=25%31-25=25R31006=R34R3=24%

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