Question

how do you find y=Ce^kt that passes through (2,100) and (5,10)

Answer 1

You get the simultaneous equations:
\[100 = Ce^{2k} \\
10=Ce^{5k}\]
Divide the second by the first and you get:
\[\frac{1}{10}=e^{3k}\]Solving for k gets:
\[k=\frac{\ln{\frac{1}{10}}}{3} \approx -0.768\]Now sub this into either of the equations and solve for C.