Return to Assignments Exponential functions and graphs

### Assignment 9

Draw the graphs of the functions:

Calculate the intersection point of both graphs.

### Solution

We already outlined in previous assignments how the graphs of both functions can be sketched.

To find the intersection point we have to solve the following equation:

We multiply both sides by and get:

We transform this equation by substituting:

Then we get:

We solved the quadratic equation by factorizing. The solutions of this equation are: or . The latter soluton does not satisfy the equation because is an exponential function and thus positive. Therefore we get the solution from the exponential equation:

From the figure we can verify that this solution is correct.