Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
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?
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Adam Moon
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
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.
View More Answers From This Book
Find Another Textbook
02:27
Mrs. Voorhees claims that Bowie knife is the most effective method of dispos…
01:39
Many consumers pay careful attention to stated nutritional contents on packa…
05:42
Using the left and right Riemann sums above, we definitively conclude that
00:31
point)Assume {U, , Uz , U3 , U4 } does not span R3Select the best st…
02:56
15. Alumni Contributions The = ation for & small director of an alumni a…
04:09
3) A fair die is rolled nine times_ What is the probability that an odd numb…
05:24
Rove 403LT} ~?3
03:14
The CDF of a random variable X is given by: F() {8 -Find the PDF oX Find…
02:06
The point Pis on the unit circle. Find P(x. y) from the given information
01:15
Solve the equation (x in radians and 0 in degrees) for all exact solutions w…
