M4.10.4 For the adult
Exponential graphs
What does the graph of y = 2ˣ look like? It starts small. How fast does it rise?
What this chapter teaches
In an exponential rule such as y = 2ˣ the letter is in the power. With a base above 1 the graph grows, faster and faster. With a base between 0 and 1 it decays towards the x axis. Every such graph passes through (0, 1) and never reaches the x axis.
Three questions to ask
There is no one right wording. Listen for the idea.
- How can you tell y = 2ˣ from y = 2x by working out y when x = 5?
- Why does every graph y = aˣ pass through the point (0, 1)?
- How do you tell a growth curve from a decay curve by looking at the base?
After the chapter, the learner can
- Draw y = 2ˣ from a table of values
- Tell a growth curve from a decay curve
What they copy into their notebook
y = aˣ passes through (0, 1) and stays above the x axis. Base above 1: growth, rising faster. Base between 0 and 1: decay, falling towards the axis.