Question

How to find the rule of this logarithm graph?

Answer 1

(3) and (4) give values of `aand b`

Explanation:

Equation of graph

`y=ae^x+b`

Two unknown `aand b`. We must have two equations.

1. Point `(1,14)` lies on the curve.

   `14=ae^1+b`
   `=>14=ae+b` ........(1)

2. Point `(0,0)` also lies on the curve.

   `0=ae^0+b`
   `=>0=a+b` ........(2)
   Subtracting (2) from (1) to eliminate `b`, we have
   `14=ae-a`
   `=>a=14/(e-1)` ......(3)
   From (2)
   `b=-14/(e-1)` .......(4)