# How do you find the exponential model #y = ae^(bx)# that fits the two points (0, 8), (1, 3)?

##### 1 Answer

It is nice that we are given the point,

Substitute the point

Any number raised to the zero power is 1:

Use the point,

The final equation is:

Often, the same problem is asked where the x coordinate of one of the points is not 0. When this happens, you must find the value of

Given, two points,

Write two equations by substituting each point into the given equation:

Divide equation [2] by equation [1]:

Please observe that

When you divide two numbers with the same base, it is the same as subtracting the exponents:

Flip the equation and use the natural logarithm on both sides:

Because

Factor out

Divide both sides by

Now that you have the value of