look at this table:
x y
0 -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
This table represents an exponential function because the y-values are decreasing exponentially as the x-values increase.
We can write the function as:
y = a(b)^x
By plugging in the given values from the table, we can find the values of "a" and "b".
For the first row, when x = 0, y = -6:
-6 = a(b)^0
-6 = a(1)
-6 = a
For the second row, when x = 2, y = -12:
-12 = a(b)^2
-12 = 6b^2 (since a = -6 from the previous calculation)
-2 = b^2
b = √(-2) (taking the square root of both sides)
Since b is negative, we can write it as b = -√2.
Therefore, the function that models the data is:
y = -6(-√2)^x