For this page, you’ll need to have Modeling Covid Spread (Desmos) open to Slide 3: Exploring Exponential Models.
The curve you’ll see is the graph of g(x), an exponential function. Another, identical curve f(x) is hiding behind it.
1 Use the starting values of a, b, and k in Desmos to complete the following equation: g(x) = f(x) =
a
(b) x +
k
Base b
2 Make sure k = 0 and a = 1. Experiment with b. For what values of b is the function undefined, with the line disappearing?
3 Keeping a = 1 and k = 0, change b to 0.5, 1, and 2, graphing each curve below. For each curve, label the coordinates at x=1, 2, and 3.
b = 0.5 |
b = 1 |
b = 2 |
4 What does b tell us about an exponential function, when b > 1?
5 What does b tell us about an exponential function, when 0 < b < 1?
Vertical Shift…and Horizontal Asymptote k
6 Keeping a = 1 and b = 2, try changing the value of k to -10, 0, and 10, graphing each curve in the squares below. For each curve, find and label the y-value where the curve is "most horizontal", then draw a horizontal line at that y-value.
k = - 10 |
k = 0 |
k = 10 |
7 What does k tell us about an exponential function?
Initial Value a
8 Set k = 0 and b = 2. Change the value of a to 10, 2, and -5, graphing each curve in the squares below.
For each curve, label the y-intercept (x=0).
a = 10 |
a = 2 |
a = - 5 |
9 What does a tell us about an exponential function?
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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