Question

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

Answer 1

Assuming your points are in the form \((t,y)\) and not the other way around, substituting each gives you simultaneous equations.
\[(t,y) = (0,4) \Rightarrow 4=Ce^{k \cdot 0}\]\[(t,y) = (5,\tfrac{1}{2}) \Rightarrow \frac{1}{2} = Ce^{k \cdot 5}\]What does this tell you about \(C\) and \(k\)?