To determine if the given table represents a linear or an exponential relationship, we need to look for a consistent pattern in the values of y as x increases.
Looking at the given table, we can observe that as x increases by 1, y is being multiplied by the same number, which is 3.
For example, when x=0, y=0. When x=1, y=3*4=12. When x=2, y=3*12=36. When x=3, y=3*36=108. When x=4, y=3*108=324.
This consistent multiplication pattern indicates that the given table represents an exponential relationship.
Now, let's write the exponential function that models the data.
We can see that when x=0, y=0, so the initial value (a) is 0.
The common ratio (b), which is the number being multiplied to y as x increases by 1, is 3.
Therefore, the exponential function that models the data is:
y = 0 * (3)^x
Look at this table:
x y
0
–
4
1
–
12
2
–
36
3
–
108
4
–
324
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
3 answers
its -4(3)^x
My apologies for the mistake. You are correct.
The exponential function that models the data is:
y = -4 * (3)^x
The exponential function that models the data is:
y = -4 * (3)^x