Step by step
The question
Question: graph y = 4 × 1.5ˣ.
1 Read a and b
This is the rule y = a times b to the power x.
a = 4 is the start: the y when x is 0.
b = 1.5 is the growth factor: each time x goes up 1, y is multiplied by 1.5.
1.5 is more than 1, so y grows.
Careful!
Power first, then times.
Only 1.5 is squared, not 4 times 1.5.
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 4 times 1, that is 4: the start.
x = 1: 1.5 to the power 1 is just 1.5.
4 times 1.5 is 6.
x = 2: 1.5 to the power 2 is 2.25.
Times 4: 9.
x = 3: 1.5 to the power 3 is 3.375.
Times 4: 13.5.
x = 4: 1.5 to the power 4 is 5.0625.
Times 4: 20.25.
Look at the y's: each one is the one before, times 1.5.
That is what exponential means.
3 Plot the points
Draw the grid.
The y numbers go up in 5s, 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 30.375.
One more step of the table: 20.25 times 1.5 is 30.375 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.