Difference between revisions of "009B Sample Midterm 1, Problem 3"

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<span class="exam">Evaluate the indefinite and definite integrals.
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<span class="exam"> A population grows at a rate
  
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::<span class="exam">a) <math>\int x^2 e^xdx</math>
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::<math>P'(t)=500e^{-t}</math>
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::<span class="exam">b) <math>\int_{1}^{e} x^3\ln x~dx</math>
 
  
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<span class="exam">where &nbsp;<math style="vertical-align: -5px">P(t)</math>&nbsp; is the population after &nbsp;<math style="vertical-align: 0px">t</math>&nbsp; months.
  
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<span class="exam">(a) &nbsp; Find a formula for the population size after &nbsp;<math style="vertical-align: 0px">t</math>&nbsp; months, given that the population is &nbsp;<math style="vertical-align: 0px">2000</math>&nbsp; at &nbsp;<math style="vertical-align: 0px">t=0.</math>
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'''Solution:'''
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<span class="exam">(b) &nbsp; Use your answer to part (a) to find the size of the population after one month.
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!Step 1: &nbsp;  
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[[009B Sample Midterm 1, Problem 3 Solution|'''<u>Solution</u>''']]
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[[009B Sample Midterm 1, Problem 3 Detailed Solution|'''<u>Detailed Solution</u>''']]
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!Step 2: &nbsp;
 
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!Final Answer: &nbsp;
 
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[[009B_Sample_Midterm_1|'''<u>Return to Sample Exam</u>''']]
 
[[009B_Sample_Midterm_1|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 10:27, 20 November 2017

A population grows at a rate

where    is the population after    months.

(a)   Find a formula for the population size after    months, given that the population is    at  

(b)   Use your answer to part (a) to find the size of the population after one month.

Solution


Detailed Solution


Return to Sample Exam

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