The total number of insects in the five generations are 1,319 insects.
- Let the insect population be P.
Given the following data;
- First generation = 100 insects.
To find the total number of insects in the five generations;
From the question, we deduced that each new generation is 1.5 times as large as the previous generation. Thus, we would multiply each of the previous generation by 1.5 using the mathematical expression;
[tex]New \; generation = 1.5[/tex] × [tex]Previous \; generation[/tex]
For the second generation:
Second generation = [tex]1.5[/tex] × [tex]100[/tex]
Second generation = 150 insects
For the third generation:
Third generation: = [tex]1.5[/tex] × [tex]150[/tex]
Third generation: = 225 insects
For the fourth generation:
Fourth generation = [tex]1.5[/tex] × [tex]225[/tex]
Fourth generation = 337.5 insects
For the fifth generation:
Fifth generation = [tex]1.5[/tex] × [tex]337.5[/tex]
Fifth generation = 506.25 insects
Next, we would calculate the total number of insects in the five generations;
[tex]Total\; insects = 100 + 150 + 225 + 337.5 + 506.25[/tex]
Total number of insects = 1318.75 ≈ 1319 insects.
Therefore, the total number of insects in the five (5) generations are 1,319 insects.
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