SOLUTION: An insect colony grow exponentially from 150 to 3000 in 4 months. How long will it take for the colony to reach 50,000? Use the formula A(m)=Pe^rt.(where time is in months)

Question 881792: An insect colony grow exponentially from 150 to 3000 in 4 months. How long will it take for the colony to reach 50,000? Use the formula A(m)=Pe^rt.(where time is in months)
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Write it this way: and know that t is number of MONTHS.

You first want to find the rate, r. Do this symbolically for substitution convenience.

Drop the notation for the t in the function name also for convenience.

NOW substitute.

maybe, but better as .

The question is find t for A(t)=50000.
Remember the step saying, ? Now, just divide left and right by r to solve symbolically for t:

and substitute the known and found values.
, which means time starting from the initial 150 colony.
months.
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