I need to show steps using a logarithmic: Exponential Growth - insects In a labo

Question

I need to show steps using a logarithmic:

Exponential Growth - insects In a laboratory experiment on the growth of insects, there were 74 insects three days after the beginning of the experiment and 108 after an additional two days. Assume that the insect population grows exponentially as modeled by the equation y = ab^t. Where y represents the number of insects some number of days (t) after the start of the experiment. The initial number of insects is represented by the letter a, and b represents the growth rate of insects.


Find: a. the initial number of insects (a)

Explanation / Answer

y=ab^t
74=ab^3
108=ab^5
ln(74/a)=3lnb
ln(108/a)=5lnb
(74/a)^1/3=(108/a)^1/5
a^(1/3-1/5)=(74^(1/3))/(108^(1/5))
a^(2/15)=1.64
a=1.64^(7.5)
a41 insects

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