Question

A rumour spread exponentially through a college. 100 people have herad it by noon, and 200 people by 1 pm. How many people have heard it by:

(a) 3pm
(b) 12.30 pm
(c) 1.45 pm?

Answer 1

doubles every hour
at noon 100
at 1 200
at 2 400
at 3 800

Answer 2

How would you write that in exponential form?

Answer 3

12:30 is a bit tricker. it is
\[100\times 2^{\frac{1}{2}}\]

Answer 4

if it doubles every hour with initial value 100 then "t" hours starting at noon, formula would be
\[100\times 2^t\]

Answer 5

so for three hours it is
\[100\times 2^3=800\] and for half an hour it is
\[100\times 2^{\frac{1}{2}}\]

Answer 6

OK. That makes sense.. and the last would be 200 x 2^3/4? Or am I wrong.. just trying to get the ahng of it...

Answer 7

yes you could write it like that

Answer 8

Thanks :) I'm beginning to understand it now!

Answer 9

You could write it as \( 100 \times 2^t \) where t is the elapsed time in *hour*.

Answer 10

or you could write
\[100\times 2^{\frac{7}{4}}\] which is the same thing.

Answer 11

Ok, thanks again!

Answer 12

yw

Answer 13

It's 45 minutes passed 1:00.. or 15 minutes to 2:00.. so it's either ratio 7/4 or 3/4 the other way round

Answer 14

Actually the answer should be 7/4 and not 3/4

Answer 15

It gives the same answer :)

Answer 16

it is the same thing

Answer 17

Mea culpa, I thought you are multiplying by 100 both times.

Answer 18

\(200 \times 2^\frac 34 = 100 \times 2 \times 2^\frac 34 = 100 \times 2^\frac 74 \)

Answer 19

you can say "at 1 it was 200 and 3/4 of an hour later it is
\[200\times 2^{\frac{3}{4}}\] or at noon it was 100 so 7/4 of an hour later it is
\[100\times 2^{\frac{7}{4}}\]
laws of exponents tell you they have to be equal because
\[100\times 2^{\frac{7}{4}}=100\times 2^1\times 2^{\frac{3}{4}}=200\times 2^{\frac{3}{4}}\]

Answer 20

what ffm said

Answer 21

Yup, I kinda figured ;) Thanks anyway.