Question

The function y=Ce^kt passes through the two points: (1,4) and (4,19). Find C and k.

Answer 1

HI :DDDD

Answer 2

Hold On one second :)

Answer 3

no problem:) I get what im supposed to do but I keep getting the problem wrong:/

Answer 4

Hm, I'm not sure either >_< I'm sorry ;-;

Answer 5

hmm its alright;) I'll just wait or ask a friend:)

Answer 6

Alrighty, I hope you find the answer soon!!!! :) good luck

Answer 7

Are you sure about that first point?

Answer 8

oops its supposed to be (1,4)

Answer 9

Okay, so the curve is given by \(y=Ce^{kt}\). You're given two points that are known to lie on the curve, \((1,4)\) and \((4,19)\).

This means you have the following equations:
\[\begin{cases}4=Ce^k\\19=Ce^{4k}\end{cases}\]
In other words, when \(t=1\) you get \(y=4\). Similarly, when \(t=4\) you get \(y=19\). Solve for \(C\) and \(k\).

Answer 10

Do I have to set the two equations equal to each other and find k first and then plug in the k into one of the equations to find C? I tried that and I kept getting the answer wrong:/ I think its probably how I did the math maybe..

Answer 11

First thing I'd do would be to find an expression for one of the variables in terms of the other. So you could solve for \(C\) and get \(C=\dfrac{4}{e^k}=4e^{-k}\), as an example.

Continuing in this manner, you would plug this into the other equation:
\[19=Ce^{4k}~~\Rightarrow~~19=4e^{-k}\times e^{4k}=4e^{3k}\\
k=\cdots\]
Then solve for \(C\).

Answer 12

hmm, ill try that method, thanks.I'll see if I can get the correct answer this time:)