Problem 18 Hard Difficulty

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?

Answer

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Video Transcript

So given the above problem, you see that this is unification of integration. We have the rate for here and the time till all I ever asked to find the population. So first we set it up with the elements and using those off integration, we integrate each confident first with this one. We have two hundred two thousand side see us then to go this confident, which is into five. Oh, I'll just free Saturday. Yes, And then we close it off of the print the city because it's easy to forget sometimes that you learn to great in both sight and have seen put in the limits. So we have that over here, and then we put in the nine and five as you do it with the integration and subtracting so doing that we have and that is supposed limits. So for this confident evaluating with a calculator you have three thirty six thousand five hundred and forty two and some decimals and then the other confident, which is this party. If you and then we subtract both of them to give you the file answer and you can round up to the required number. That's more plate is. But I just chose to be things that's an example. So this would be your final answer