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.
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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where did the 900^2 come from in part c? Please explain . Thank you
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