Look at this table:
x y
0
–
3
1
–
6
2
–
12
3
–
24
4
–
48
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine whether the data follows a linear or exponential pattern, we need to observe the relationship between the values of x and y.
Looking at the table:
For every increase in x by 1, y is multiplied by a factor of 2.
This indicates an exponential relationship.
The general form of an exponential function is y = a(b)^x.
To find the specific values of a and b, we can plug in x = 0 and y = 3 into the equation to solve for a and b.
3 = a(b)^0
3 = a(1)
a = 3
Therefore, the exponential function that models the data is:
y = 3(2)^x