where did the 900^2 come from in part c? Please explain . Thank you 2. Some psychologists have said that the number of new facts a person can remember afterhours is given by(a) How many facts are remembered after one hour?90Solution: f(1) = 99-90 = 10.f' (t)(b) What is the rate at which the number of facts remembered is changing after 1 hour?Solution: Let's compute the derivative of f:=f(t) ==90t99t - 90=(99t-90) (90t)' - (90t) (99t-90)'(99t-90)²(99t90) (90) - (90t) (99)(99t-90)²8910t8100 - 8910t(99t – 90)²-8100(99t – 90)²So we get f'(1) = -810081= -100.(c) What is the rate it's changing after 10 hours?Solution:Using what we did in part b, f'(10) =-8100 -0.01(900)²-(d) Why is the rate of change so much smaller after 10 hours, compared to 1 hour?Solution: After 10 hours one has probably forgotten most of the new facts, so they areforgetting them at a much slower rate.

2. Some psychologists have said that the hours is given by f(t)= (a) How many facts are remembered after one hour? Solution: f(1) = 9990 = 10. 90 (b) What is the rate at which the number of facts remembered is changing after 1 hour? Solution: Let's compute the derivative of f: (99t-90) (90t)' (90t) (99t-90)' f' (t) So we get f'(1) == 81000 90t 99t-90 = (99t-90)² (99t-90) (90) (90t) (99) (99t-90)² 8910t8100 - 8910t (99t-90)² = -100. -8100 (99t-90)² (c) What is the rate it's changing after 10 hours? Solution: Using what we did in part b, f'(10): - -8100 (900)2 -0.01 (d) Why is the rate of change so much smaller after 10 hours, compared to 1 hour? Solution: After 10 hours one has probably forgotten most of the new facts, so they are ting them at a much slower rate.

2. Some psychologists have said that the hours is given by f(t)= (a) How many facts are remembered after one hour? Solution: f(1) = 9990 = 10. 90 (b) What is the rate at which the number of facts remembered is changing after 1 hour? Solution: Let's compute the derivative of f: (99t-90) (90t)' (90t) (99t-90)' f' (t) So we get f'(1) == 81000 90t 99t-90 = (99t-90)² (99t-90) (90) (90t) (99) (99t-90)² 8910t8100 - 8910t (99t-90)² = -100. -8100 (99t-90)² (c) What is the rate it's changing after 10 hours? Solution: Using what we did in part b, f'(10): - -8100 (900)2 -0.01 (d) Why is the rate of change so much smaller after 10 hours, compared to 1 hour? Solution: After 10 hours one has probably forgotten most of the new facts, so they are ting them at a much slower rate.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.EA: Extended Application Managing Renewable Resources

Problem 2EA

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