Question

The number of butterflies in a forest stretch near the highway was estimated to be 16,000. The population of butterflies in the area follows an annual birth rate of 10% with a mortality rate of 5% every year. How many butterflies will be there in the stretch after 3 years?

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Answer 1

Step-by-step explanation:

Solution:

Note that, the actual growth rate of the butterflies = annual birth rate - mortality rate

Growth rate of the butterflies in the forest stretch

$\bf=(10-5)\% \: p.a. \: 5\% p.a.$

We have, butterflies count after 3 years

$\sf=16000(1+ \frac{5}{100} )^ 3 \\ \sf=16000(1+ \frac{1}{20} )^ 3 \\ \sf =16000( \frac{21}{20} )^ 3 =18522$

Thus, after 3 years the number of butterflies in the forest stretch near the highway will be 18, 522.