A news item is spreading by word of mouth through a population of size 35,000 people. Aftertdays, the number of people (in thousands) who have heard the news is given by the following equation.

y = f(t) = 35/(1+125e^-0.35t)

(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 derivativef'(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 functionf(t) to the solutions to the different forms of the logistic growth model from this lesson. Enter the differential equation in terms ofythat corresponds to this solution.

dy/dt=

(e) How many people have heard the news when its rate of spread is 3.0525 thousand people per day? (There are two answers. Give your answers correct to the nearest whole person.)

? people (smaller value)

? people (larger value)

(f) At what two times is the news spreading at rate 3.0525 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