Question

A news item is spreading by word of mouth through a population of size 20,000 people. After t days, the number of people (in thousands) who have heard the news is given by the following equation. f(t) = 20/(1+125e^(-.6t)) (a) Approximately how many thousand people have heard the news after 9 days? (Give your answer correct to at least three decimal places.) ___ thousand people (b) Calculate the derivative f'(t). f'(t) = _ (c) At what rate is the news spreading after 11 days? (Give your answer correct to at least four decimal places.) _ thousand people per day (d) Compare the function f(t) to the solutions to the different forms of the logistic growth model from this lesson. Enter the differential equation in terms of y that corresponds to this solution. dy/dt = (e) How many people have heard the news when its rate of spread is 2.9325 thousand people per day? (There are two answers. Give your answers correct to the nearest whole person.) people (larger value) (f) At what two times is the news spreading at a rate of 2.9325 thousand people per day? (Give your answers correct to at least three decimal places.) _ days (smaller value) _ days (larger value) (g) What is the fastest rate at which the news spreads? (Give your answer correct to at least three decimal places.) ______ thousand people per day

          A news item is spreading by word of mouth through a population of size 20,000 people. After t days, the number of people (in thousands) who have heard the news is given by the following equation.

f(t) = 20/(1+125e^(-.6t))

(a) Approximately how many thousand people have heard the news after 9 days? (Give your answer correct to at least three decimal places.)
_______ thousand people

(b) Calculate the derivative f'(t).
f'(t) = _________

(c) At what rate is the news spreading after 11 days? (Give your answer correct to at least four decimal places.)
___________ thousand people per day

(d) Compare the function f(t) to the solutions to the different forms of the logistic growth model from this lesson. Enter the differential equation in terms of y that corresponds to this solution.
dy/dt = __________

(e) How many people have heard the news when its rate of spread is 2.9325 thousand people per day? (There are two answers. Give your answers correct to the nearest whole person.)
______ people (larger value)

(f) At what two times is the news spreading at a rate of 2.9325 thousand people per day? (Give your answers correct to at least three decimal places.)
_____ days (smaller value)
_____ days (larger value)

(g) What is the fastest rate at which the news spreads? (Give your answer correct to at least three decimal places.)
________ thousand people per day

Added by Marina J.

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