Difference between revisions of "009B Sample Final 3, Problem 3"

Revision as of 10:55, 18 February 2017

The population density of trout in a stream is

\rho (x)=|-x^{2}+6x+16|

where $\rho$ is measured in trout per mile and $x$ is measured in miles. $x$ runs from 0 to 12.

a) Graph

\rho (x)

and find the minimum and maximum.

b) Find the total number of trout in the stream.

Solution:

(a)

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

@@ Line 1: / Line 1: @@
-<span class="exam">Consider the region bounded by the following two functions:
+<span class="exam">The population density of trout in a stream is
-::::::::<span class="exam"> <math style="vertical-align: -5px">y=2(-x^2+9)</math> and <math style="vertical-align: -4px">y=0</math>.
-<span class="exam">a) Using the lower sum with three rectangles having equal width, approximate the area.
+::::<math>\rho(x)=|-x^2+6x+16|</math>
-<span class="exam">b) Using the upper sum with three rectangles having equal width, approximate the area.
+<span class="exam">where <math>\rho</math> is measured in trout per mile and <math>x</math> is measured in miles. <math>x</math> runs from 0 to 12.
-<span class="exam">c) Find the actual area of the region.
+::<span class="exam">a) Graph <math>\rho(x)</math> and find the minimum and maximum.
+::<span class="exam">b) Find the total number of trout in the stream.
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"