What is the exponential function y=Ce^kt that passes through two given points?

Question

Find the exponential function y = Ce^kt  that passes through the two given points. (Round the value of k to four decimal places.) 

Points: (0,3) and (4,2)

Answer 1

I assume your points are given as (t, y)---i.e. the independent variable first.

since you are given 2 points, you can write 2 equations where C and k are the unknowns:

Using (0, 3): 3 = Ce^0*k = C⁰ = C ---> C = 3

Using (4, 2): 2 = 3e^4k

e^4k = 2/3

take the ln of each side:

4k = ln(2/3) = -.4055

k = -.1014

So, the equation is : y = 3e^-.1014t