Solve for Y=Ae^kt

if Y=20747 t=12

and Y=28619 t= 14

Question

Solve for Y=Ae^kt

if Y=20747 t=12

and Y=28619 t= 14

anonymous · Answer

Plug in get two equations and two unknowns.
20747=Ae^(12k)   28619=Ae^(14k)
Solve for A:
A=20747e^(-12k)
Plug in to other equation.
28619=20747e^(14k)e^(-12k)
28619=20747e^(2k)
Solve:
28619/20747=e^2k
ln(28619/20747)=2k
k=(1/2)ln(28619/20747)=.16

Then plug in k to solve for A
A=20747e^(-12*.16)=3041.7

anonymous · Answer

Make sense? x.x

anonymous · Answer

I get what you did but it's kind of wrong if i graph it. I have all the data points and a scatter plot on excel do you think you could take a look at it? It'll be much appreciated!

anonymous · Answer

I have no idea man, you could do my method and do multiple points and get an average value for k and A.

anonymous · Answer

before you put any values into the equation, take natural logarithm on both sides of the equation. Then you will get rid of exponential function and it will be simple algebraic equation. 
You will get 
$$\ln Y = \ln A +kt$$
take ln(A) as a separate variable, say b; i.e. b= ln(A)
$$\ln Y = b +kt$$
Then substitute data points and solve the two equations for b and k, by either elimination or graphing or substitution.  
Once you get b, you can easily calculate A.

anonymous · Answer

oh thanks chenna