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Sketching an Exponential Function and Solving an Exponential Equation
The mathematical solution explains how to sketch the graph of an exponential function. Explanation of the graph being an increasing exponential is given and the fact that y=0 is an asymptote is discussed. The intersection point with the y axis is found and, using the information given, the graph is sketched.
The second part of the question requires students to solve an exponential equation by expressing the equation as a quadratic. The quadratic equation is factorised with the resultant equations being solved using simple logarithms.
The graphical solution explains how to use the graphic calculator to verify the accuracy of the sketch by confirming the point of intersection with the y-axis and that there are no roots as y=0 is an asymptote. The solutions to the equation are verified by drawing the appropriate graph and finding the points of intersection with the x-axis.
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