How would I write an exponential function that passed through two given points? How exactly do I determine it?

Answer 1

Suppose y = a e ^bx

Then ln y = ln a + ln (e ^bx) = ln a + bx

So if you have two point (x1, y1) and (x2,y2)

Substitute the two points into ln y = ln a + bx

This gives two equations in two variables (ln a, b)

Solve the two equations giving ln a, b

Knowing ln a, you can find a

a = e^{ln a}

Then you know a, b, defining the exponential function