**Unformatted text preview: **roblems 11 - 14, use the scenarios in questions 6 - 8 to draw a velocity-time graph which
presents the motion described on the grids below. Draw the horizontal axis. Label the axes
propriately with units and scale.
#
P (t )
1. A raccoon population in a southern region varies due
to fluctuating food supplies. Assume the number of
raccoons, P(t), is given by P(t) = 250 + 150 sint
where t is the time, in years. Store the function for P(t)
as Y1 in your calculator. Use the window of [0, 10] for
t, to sketch the graph. On the sketch, show a point
where P(t) is increasing, decreasing, and a point
where it is not changing much.
2 76. 047- 250 - 2. 6047
4 , in Fears $ $4 10
10
12. Estimate the average rate of change of the raccoon population for t = 1 . The change in
R(t) from 1 year to tis P(t) - P(1). So, the average rate of change for P(t) changes at the
average rate r(t) given by r(t) =Complete the table of values of r (t) for each estimate.
A.) Complete the table below to determine which is the best approximation?
P ( 1.1 ) - P ( )
1. 1 - 1
B.) What does this rate mean regarding the raccoon population?
This rate means the Population is fluctuating
P ( 1 ) = 252 . 618 P ( , 91 ) = 252, 522 P ( 1,001 ) = 252, 620
t
P(.99) - P(1)
P(1.001) - P(1)
P(1.1) - P(1)
.99 - 1
1.001 - 1
1.1 - 1
r (t )
2. 6
2
2. 61
13. The instantaneous rate of change of P(t) at t = 1 is the limit that r (t) approaches as t
approaches 1 [the limit of the average rates at t = 1] . Use the numerical derivative feature
to determine the instantaneous rate at t = 1.
1.01 1. 001
3.76, 301 - 376. 221 = 80 377.624
376. 221
1.001 - 1
377.024-376 22/
1.01-1
14. Approximate the instantaneous rate the raccoon population is changing at't = 4.
Explain why the answer is negative. 4 .o1 4. ool
135. 505
4.01 - 4
135. 505, 136. 301, 136. 47 9
136 321 - 136, 479
-97.4
4.001 - 4
@ 2016 Flamingo Math"
The answer is negative the racans are leaving...

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- Spring '16
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