SP#3: Unit I Concept 1: Solving an Exponential Equation

 

Let me be honest, solving these type of problems wasn't easy. First you need to understand how to find the values of the following variables. ( a, b, h, and k). This is because they are important  to finding the asymptote, domain, and range. You also need to focus on the colored parts of the image, because they are important. They are meant to help you

 

 



Step 1: The equation can determine if the graph lies below or above the asymptote. Since the value of a is negative, the graph lies below the asymptote; then check if the asymptote is vertical or horizontal by checking to see if its a log or exponential. In either case, the equation is an exponential one, and it's asymptote is equal to the k value. Therefore, the asymptote is "y = -4"
Step 2: Now since the asymptote we can say there is no x intercept.
Step3: Solve for the y-intercept.
Step 4: Next; determine the domain and range of the graph. Since this is an exponential equation, the domain is unrestricted. The range, however, depends on the asymptote. In this case, the range is -∞, -4.
Step 5: Label the graph, plug the equation into your graphing calculator and press the buttons labeled '2ND' and 'TABLE'. This will give you a table of all the points on the graph. Select a few, put them in your table, and plot them. Draw the asymptote, connect the dots, now you have solved this exponential equation.