Question

(Need 3 answers) An entomologist discovered a new insect species. The population of the insect species can be modeled by P(n) = 3,450 · bn, where n is the number of days and b is an unknown positive base.

Based on the model, there were initially ?
insects.

If b = 1.75, the daily percent growth rate of the new insect would be ?
%.

If there are 55,200 new insects after 4 days, then b = ?
.

Answer 1

Based on the model, there were initially ?

insects. = 3450 insects

If b = 1.75, the daily percent growth rate of the new insect would be ?

%. = 75%

If there are 55,200 new insects after 4 days, then b = ? =2

Explanation:

Answer 2

• See below

Explanation:

According to the model, the equation is:

• P(n) = 3450*bⁿ

Based on the equation, the initial number of insects is 3450

If b = 1.75, daily growth rate is:

• 1.75 - 1 = 0.75 = 75%

If we get P(4) = 55200, find the value of b:

• 55200 = 3450*b⁴
• b⁴ = 55200/3450
• b⁴ = 16
• b⁴ = 2⁴
• b = 2