Look at this table:
x y
1 6
2 12
3 24
4 48
5 96
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
Looking at the table, it is clear that as x increases, the corresponding values of y are also increasing but at an increasingly faster rate. This indicates that the relationship between x and y is exponential.
We can find the values of a and b by analyzing the pattern in the table. When x=1, y=6. This suggests that when x=0, y would be equal to 6 divided by b. Let's calculate this:
When x=0, y=6/b.
Now let's find how much y changes each time x increases by 1. We can compare the values of y to see that it is doubling each time:
Second row: 12 is double of 6
Third row: 24 is double of 12
Fourth row: 48 is double of 24
Fifth row: 96 is double of 48
This means that when x increases by 1, y is doubling. Therefore, b must be equal to 2.
Now we can substitute this value of b into the equation we discovered earlier:
When x=0, y=6/b
When x=0, y=6/2
When x=0, y=3
Thus, we have a=3.
The exponential function that models the data is:
y = 3 * (2^x)
Is that 3 x (2^x)
Apologies for the confusion in my previous response. You are correct, the correct exponential function that models the data is:
y = 3 * (2^x)