How do I find the equation of the exponential line that goes through all points?

Iconaguard May 18, 2022

#1**+1 **

Let \(y = a\cdot b^x +c\) for some constants a, b, and c

Substitute (x, y) = (0, 900) (x, y) = (5, 200) and (x, y) = (4, 450) to get the system of simultaneous equations \(\begin{cases}a + c= 900\\a\cdot b^4 + c=450\\a\cdot b^5 + c=200\end{cases}\).

It is really hard to find the exact solutions of this system of equations, but the approximate solution is (a, b, c) = (-147.7, 1.418, 1047.75).

Here's the graph:

MaxWong May 18, 2022