Find the exponential function
y = Ce^kt
that passes through the two given points.

(0,5) (4,1/2)

Question

Find the exponential function 
y = Ce^kt
 that passes through the two given points.

(0,5) (4,1/2)

anonymous · Answer

the slope is -1/8

anonymous · Answer

C is equal to 5

johnweldon1993 · Answer

Correct C = 5, what about 'k' ?

anonymous · Answer

and what is the rest of the variables equal to

anonymous · Answer

I don't know, I had a very difficult time finding k because I was thrown off with the zero. I got $$k = \frac{\ln(.1)  }{ 4 }$$

johnweldon1993 · Answer

That is absolutely correct, i know its a sloppy decimal but it is correct!

anonymous · Answer

so the decimal is equal to -.5756

anonymous · Answer

how do i find the y function?

johnweldon1993 · Answer

Yes k = that decimal

And you already have, since you know both of these points are on this exponential curve, by solving each individual equation that we did we have found the function that contains both points

By first solving for C...we found to equal 5....we knew that the function we were looking for had to be in SOME form of

$\large y = 5e^{kt}$

Then how we just solved for 'k' ...and found it to be -0.5756 we now have the exact function we need

$$\large y = 5e^{-0.5756t}$$

How do we know it is correct? Plug in both your points again and see if it checks out!

anonymous · Answer

Oh wow, I completely get it now! Thank you so much!

johnweldon1993 · Answer

No problem :)