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

From Grad Wiki
Jump to navigation Jump to search
(Created page with "<span class="exam">Divide the interval <math>[0,\pi]</math> into four subintervals of equal length <math>\frac{\pi}{4}</math> and compute the right-endpoint Riemann sum of <ma...")
 
 
(22 intermediate revisions by 2 users not shown)
Line 1: Line 1:
−
<span class="exam">Divide the interval <math>[0,\pi]</math> into four subintervals of equal length <math>\frac{\pi}{4}</math> and compute the right-endpoint Riemann sum of <math>y=\sin (x)</math>
+
<span class="exam"> A population grows at a rate
  
 +
::<math>P'(t)=500e^{-t}</math>
  
−
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+
<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.
−
!Foundations: &nbsp;  
 
−
|-
 
−
|1)
 
−
|-
 
−
|2)
 
−
|-
 
−
|-
 
−
|Answers:
 
−
|-
 
−
|1)
 
−
|-
 
−
|2)
 
−
|}
 
  
−
'''Solution:'''
+
<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>
−
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+
 
−
!Step 1: &nbsp;  
+
<span class="exam">(b) &nbsp; Use your answer to part (a) to find the size of the population after one month.
−
|-
+
<hr>
−
|
+
[[009B Sample Midterm 1, Problem 3 Solution|'''<u>Solution</u>''']]
−
|-
+
 
−
|
+
 
−
|-
+
[[009B Sample Midterm 1, Problem 3 Detailed Solution|'''<u>Detailed Solution</u>''']]
−
|
 
−
|-
 
−
|
 
−
|}
 
  
−
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
−
!Step 2: &nbsp;
 
−
|-
 
−
|
 
−
|-
 
−
|
 
−
|-
 
−
|
 
−
|-
 
−
|
 
−
|}
 
  
−
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
−
!Final Answer: &nbsp;
 
−
|-
 
−
|
 
−
|-
 
−
|
 
−
|}
 
 
[[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

Retrieved from "https://gradwiki.math.ucr.edu/index.php?title=009B_Sample_Midterm_1,_Problem_3&oldid=4122"