Question

Find the exponential function y = Cekt that passes through the two given points.(see attached)

Answer 1

y = Ce^kt
y = 5/6 e^ 6k
10 = 5/6 e^6k
ln 10 = 30/6k
ln 10 = 5k
ln(10)/5 = k

y = 5/6e ^(ln(10)/5) t

y = 5/6e ^4605t

Answer 2

Apparently this isn't right... :(

Answer 3

to find the equation you need to solve for C & k

plug in x=0, y=5/6
& x=6, y=10

to solve:

Answer 4

which I did. Was I correct?

Answer 5

You plugged them into the wrong place.
The 2 equations should be
5/6 = Ce^0
10 = Ce^(6t)

Answer 6

ok i follow you now
\[\LARGE 10 = \frac56 e^{6k}\]

correct so far...

Answer 7

yes

Answer 8

\[\Large \implies {10\cdot 6 \over 5}=e^{6k}\]

Answer 9

ah that's where I messed up.

Answer 10

ln(60)/5 = 6k

Answer 11

ln(60)/30 = k

Answer 12

or if you wanted to take ln before this step it should have been
\[\Large \ln(10)=\ln \left( \frac56 \right)+6k\]

Answer 13

I think we will stick with the other way :).

Answer 14

no...
ln(60/5)=6k

or
\[\Large \ln(12)=6k\]

Answer 15

ah :) ln(12)/6? = k

Answer 16

yes

Answer 17

alrighty I think I got this now thanks !!! :).