look at this table:
x 0 1 2 3 4
y 2 6 18 54 162
Write a linear function (y = mx + b) or an exponential function (y=a(b)^x) that models the data
From the given table, it can be observed that the value of y increases significantly with each increase in x. This suggests that an exponential function, rather than a linear function, would be more appropriate to model the data.
The general form of an exponential function is y = a(b)^x, where a and b are constants. To determine the specific values of a and b, let's examine the data further.
From the table:
When x = 0, y = 2
When x = 1, y = 6
When x = 2, y = 18
When x = 3, y = 54
When x = 4, y = 162
Observe that as x increases by one, y is being multiplied by a constant factor. In this case, it appears that y is being multiplied by 3 each time.
Thus, we can determine the values of a and b for the exponential function as follows:
a = 2 (the initial value of y when x = 0)
b = 3 (the constant factor by which y is being multiplied)
Therefore, the exponential function that models the data is:
y = 2 * (3)^x