889BCA98-F53D-427B-9F03-43FAE4E4F49A.jpeg - roblems 11 14 use the scenarios in questions 6 8 to draw a velocity-time graph which presents the motion

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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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