Question

The number of people in a town of 10,000 who have heard a rumor started by a small group of people is given by the following function:

N(t) = 10,000/(5 + 1245e-^.97t)

How long before 1000 of the people in the town have heard the rumor?

Answer 1

man they really reach for these world problems, don't they?

Answer 2

they really do, it confuses me every time

Answer 3

@satellite73 do you know how i would begin to solve this?

Answer 4

yes, set the expression equal to 1000 and solve for \(x\)

Answer 5

set this exual to 1000? N(t) = 10,000/(5 + 1245e-^.97t)

Answer 6

yes

Answer 7

\[\frac{10,000}{5+1245e^{-.97t}}=1000\] is the first step

Answer 8

and solve for t right?

Answer 9

yes

Answer 10

maybe next step would be
\[10=5+1245e^{-.97t}\]

Answer 11

okay thanks, so after that step i would solve for t? or before?

Answer 12

i got t=0.0106

Answer 13

that seems unlikely

Answer 14

im not sure i used a calculator

Answer 15

starting with
\[10=5+1245e^{-.97t}\] what did you do next?

Answer 16

i put it into a calculator and solved for t and it gave me 0.0106

Answer 17

yes, i think there must be some mistake here

Answer 18

yes, thank you so much for your help anyways. i can wait and ask the teacher because they left me without any formulas or anything

Answer 19

lets make sure it is right, it is not that hard

Answer 20

\[10=5+1245e^{-.97t}\] subtract 5\[5=1245e^{-.97t}\] divide
\[\frac{5}{1245}=\frac{1}{249}=e^{-97t}\]
\[-.97t=\ln(\frac{1}{249})=-\ln(249)\]
\[t=\frac{\ln(249)}{.97}\]

Answer 21

thank you again, i understand it much better now