Asked by Tyler

A university is doing a study to record the growth of mosquitos. There is originally 25 mosquitoes. The growth of the mosquitos is 0.03% every 7 days. How many days until there are 20 435 mosquitos?

What I did was use the growth formula A=25(1+0.03)^t to figure out how many mosquitoes were there after a week, ( I got 25.75) then used the formula A=25.75(1.03)^t/7 and got 1580. Did I do this right?
Answered by bobpursley
20435=25(1+.03)^t/7

1.03^t/7=817.4

take the log of each side.

t/7 * log 1.03 = log 817.4

t= 7* log 817.4 /log1.03

I get about 1600 days for the longer period. I agree with you.
Answered by Tyler
okay, good, I think i did it right then (it was actually a question on my exam that I just completed, it was the only question I was unsure about)
Answered by Reiny
Yes
good job, you must have done some rounding

what you want is
20435 = 25(1.03)^t , where t is the number of weeks
8174 = 1.03^t
take log of both sides
log 817.4 = log (1.03^t)
t = log 817.4 / log 1.03 = 226.87 weeks
or
1588 days
Answered by Tyler
Yeah probably, I also don't remember if it was 20435 or 20425 exactly, but it was approximately that.
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