Step by step
The question
Question: graph y = 3ˣ.
1 Read a and b
This is the rule y = a times b to the power x.
a = 1 is the start: the y when x is 0.
b = 3 is the growth factor: each time x goes up 1, y is multiplied by 3.
3 is more than 1, so y grows.
2 Make a table
We make a table: x from 0 to 4.
x = 0: anything to the power 0 is 1.
So y is 1: the start.
x = 1: 3 to the power 1 is just 3.
So y is 3.
x = 2: 3 to the power 2 is 9: 9.
x = 3: 3 to the power 3 is 27: 27.
x = 4: 3 to the power 4 is 81: 81.
Look at the y's: each one is the one before, times 3.
That is what exponential means.
3 Plot the points
Draw the grid.
The y numbers go up in 10s, because y gets big fast.
Put the points from the table on the grid.
4 Draw the curve
Join the points with a smooth curve.
It goes up faster and faster.
5 Check
Let's check with one more x.
The rule with x = 5 gives 243.
One more step of the table: 81 times 3 is 243 too.
It works!
Let's look back.
First: read a and b.
Then: make a table.
Then: plot the points.
Then: draw the curve.
Last: check.