009B Sample Final 3, Problem 3

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.

Foundations:
What is the relationship between population density  $\rho (x)$  and the total populations?
The total population is equal to  $\int _{a}^{b}\rho (x)~dx$
for appropriate choices of  $a,b.$

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

Return to Sample Exam