Example 1
If a pendulum swings to 90% of its height on each swing and starts out at a height of 60 cm, what is the equation that models this scenario? What is its graph?
- Read the problem statement and then reread the scenario, identifying the known quantities.
- Substitute the known quantities into the general form of the exponential equation , where a is the initial value, b is the rate of decay, x is time (in this case swings), and y is the final value.
- Create a table of values.
- Set up the coordinate plane.
- Plot the points on the coordinate plane and connect the points with a line (curve). When the points do not lie on a grid line, use estimation to approximate where the point should be plotted. Add an arrow to the right end of the line to show that the curve continues in that direction toward infinity.