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A hot, wet summer is causing a mosquito population explosion in a lake resort area. The number of mosquitoes is increasing at an estimated rate of $2200+10 e^{0.8 t}$ per week (where $t$ is measured in weeks). By how much does the mosquito population increase between the fifth and ninth weeks of summer?

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05:16

Abigail Darko

Calculus 2 / BC

Chapter 8

Further Applications of Integration

Section 4

Applications to Economics and Biology

Applications of Integration

Campbell University

Idaho State University

Boston College

Lectures

01:09

A hot, wet summer is causi…

03:09

02:18

00:49

An unusually wet spring ha…

02:44

Uninhibited Growth The pop…

02:40

Insect survival and renewa…

08:21

Growth of an Insect Popula…

03:54

Growth of a Colony of Mosq…

04:47

All right, so you have a mosquito growth problem here, and moskitoes are good for some things, which would be food for animals that for tourists. We do need to keep track of that. So we've got our equation: 2200 plus 10 times e to the power of .8 t and t stands for time in weeks, which is nice, and we not say this was in second it's in 1 week, but we don't have to do a conversion there. It looks like at the very beginning, before a week 1 there was 222200 mosquitoes, so they're going to exponentially grow from this point on, and we want to know how much both happens from 5 to 9 weeks, not the total number of mosquitoes that exist. That 9 weeks, but how many, how much increase occurs? So that's a little bit different. So what we need to do here is we need to look at it terms of. What'S the i'm just going to call it m for mosquitoes, the number of mosquitoes at the time of 5 weeks is equal to 2200 plus 10 times e to the .8 times 5 power, and then we're going to compare that to what happened at week 92200. Using the same function again just for week 9 and substituting night for t 0.8 times 9, all right so now we just need to do some work on the calculator here. So i'm gonna start with e to the 20 times 5 poles and the times that by 10 and add to 2200 point. So i've got 2746 around to whole mosquito because there's no such thing as a .98 mosquito. So all round up and then we've got the same equation except now: wendt 9 times .8, so e to the .8 times 9 times, 10 plus 2200, and now we have 15594 round down. So the change in mosquitoes is going to be 15594 point. That was our final count minus the initial count of 20746, and this will give us our answer. I put 45 bixio to 12848, ms and i'm thinking that that's the malt class i'm used to teaching physics were around this 2. Some significant figure cause 2200 is only 2 digits, but i'm gonna leave it around 12848 to tiotjonto the whole number since it's down to this ito. I hope that was helpful and us know if you have any other questions.

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