a.
\Find the amplitude of the function.
\The population of a certain species of a deer can be modeled by , where
is the population and
is the time in years.
Compare the function with
.
Amplitude is .
The amplitude represents the amount that the population varies above and below the initial population of .
b.
\Period .
The period represents the population will return to its original value every years.
c.
\The function is .
Make the table of values to find ordered pairs that satisfy the function.
\Choose values for and find the corresponding values for
.
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
\
| \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
Graph :
\1. Draw a coordinate plane.
\2. Plot the coordinate points.
\3. Then sketch the graph, connecting the points with a smooth curve.
\a.
\Amplitude is .
The amplitude represents the amount that the population varies above and below the initial population of .
b.
\Period is .
The period represents the population will return to its original value every years.
c. \ \
\Graph of the function is :