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 will it be until 1,000 of the people in the town have heard the rumor?

Answer 1

Replace N(t) with 1000 and solve for t

Answer 2

@Mertsj thanks, i got t=-2.1188

Answer 3

then if i plug that back in i get 11721.8072
is that the final answer?

Answer 4

Your answer should not be negative. The question asks how long it will be. So t which is time, is the answer to the question the problem asks.

Answer 5

can you please tell me what it is?

Answer 6

Why does the problem have 10000/5 instead of 2000?

Answer 7

\[N(t)=\frac{10,000}{5}+1245e ^{(-.97t)}\]

Answer 8

Is that the given equation?

Answer 9

yes that is correct @Mertsj

Answer 10

no sorry that is wrong

Answer 11

the equation is:

Answer 12

\[5000+1245000e ^{-.97t}=10000\]
\[1245000e ^{-.97t}=5000\]
\[e ^{-.97t}=.0040\]
\[-.97t \ln e=\ln .0040\]
\[-.97t=-5.517\]
t=5.688

Answer 13

thank you so much, so in that case how do i find (How long will it be until 1,000 of the people in the town have heard the rumor?)

Answer 14

@Mertsj

Answer 15

What does t represent?

Answer 16

i dont know :(

Answer 17

@Mertsj

Answer 18

Ah ha. That is your problem.

Answer 19

Did you post the entire problem or was there more words that you didn't include?

Answer 20

t is the time. When the problem says "how long will it be" it is asking you for the time. So now we have found that it will be 5.688 hours? days? until 1000 people have heard the rumor. The time units are not given unless there is more to the problem that you didn't post.

Answer 21

that is the entire problem, it must be 5 hours then because there is no other information given @Mertsj