Look at this table:
x y
0 1
1 2
2 4
3 8
4 16
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
Looking at the table, we notice that y is growing exponentially as x increases. Therefore, an exponential function would be appropriate for modeling the data.
Let's find the values of a and b in the exponential function y = a(b)^x:
As x increases by 1, y is multiplied by 2 each time. This suggests that b = 2.
To find the value of a, we can plug in one of the x and y values into the equation and solve for a. Let's use the first row of data (0, 1):
1 = a(2)^0
1 = a(1)
Since any number to the power of 0 is 1, we can simplify the equation to:
1 = a
Therefore, a = 1.
Now we have a = 1 and b = 2, so the exponential function that models the data is:
y = 1(2)^x