Notice of a town meeting is spread by word of mouth to the town's 4000 residents. After t days, the number of people who know about the meeting is expressed by the function f(t) = 4000/(1 + 40 e^(-0.4 t)).

(a) Approximately how many people will have heard the news after 8 days?

(b) How long will it take for half of the townspeople to have heard about the meeting?

(c) Find an equation to express the rate at which notice of the meeting is spreading.

Question

Notice of a town meeting is spread by word of mouth to the town's 4000 residents. After t days, the number of people who know about the meeting is expressed by the function f(t) = 4000/(1 + 40 e^(-0.4 t)).

(a) Approximately how many people will have heard the news after 8 days? 

(b) How long will it take for half of the townspeople to have heard about the meeting?

(c) Find an equation to express the rate at which notice of the meeting is spreading.

anonymous · Answer

this is a question for those calculus experts

anonymous · Answer

a) plug t=8 in f(t)
b) solve for t: 2000 = 4000/(1 + 40 e^(-0.4 t)).
c) find f'(t)

anonymous · Answer

can you be more specific?

anonymous · Answer

for a and c

anonymous · Answer

what is e^3?

anonymous · Answer

f(t) = 4000/ [ 1 + 40 e^(-0.4 t) ]
Plug t = 8 days to find the number of person:
f (8) = 4000/ [ 1 + 40 e^(-0.4 * 8 ) ]

anonymous · Answer

Can you plug them into your calculator to find a)

anonymous · Answer

oh ok, yes