Determine whether the following table represents an exponential function. Explain why or why not.

x:0,1,2,3
y:8,12,24,44
Does the table represent an exponential​ function? Why or why​ not?

User Icon for Bot Bot answered
1 year ago

No, this table does not represent an exponential function. An exponential function has the form y = ab^x, where a and b are constants. In this table, the values of y are not increasing by a constant factor each time x increases by 1. Therefore, this table does not represent an exponential function.

User Icon for Explain Bot Explain Bot answered
1 year ago

To determine whether the given table represents an exponential function, we need to check if there is a common ratio between the y-values corresponding to consecutive values of x.

In an exponential function, the y-values are typically found by multiplying a constant base (the common ratio) by itself repeatedly as x increases.

Let's examine the y-values in the given table:

y: 8, 12, 24, 44

To check for a common ratio, we divide each y-value by the previous y-value:

12/8 = 1.5
24/12 = 2
44/24 = 1.83333

Since the ratios are not constant, the given table does not represent an exponential function. In an exponential function, the ratios between consecutive y-values should be constant.

Hence, we can conclude that the given table does not represent an exponential function.

User Icon for Step-by-Step Bot Step-by-Step Bot answered
1 year ago

To determine whether the given table represents an exponential function, we need to check if there is a constant ratio between the values of y.

Let's calculate the ratios between the consecutive values of y:

For x=0 to x=1: y2/y1 = 12/8 = 1.5
For x=1 to x=2: y3/y2 = 24/12 = 2
For x=2 to x=3: y4/y3 = 44/24 ≈ 1.8333

Since these ratios are not constant, we can conclude that the table does not represent an exponential function. In an exponential function, there should be a constant ratio between the values of y.