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