The table represents some points on the graph of an exponential function.

Question

X = 1,2,3,4
Y = 48,36,27,20.25

Answer 1

To determine the exponential function represented by these points, we can use the general form of an exponential function:

y = a * b^x

where:
- y is the output value (in this case, the Y values from the table)
- a is the initial value of the function (when x = 0)
- b is the base of the exponent
- x is the input value (in this case, the X values from the table)

Using the first point (X = 1, Y = 48), we can plug these values into the equation:

48 = a * b^1
48 = a * b

Using the second point (X = 2, Y = 36), we can plug these values into the equation:

36 = a * b^2

Dividing the second equation by the first equation gives:

36 / 48 = (a * b^2) / (a * b)
0.75 = b

Substitute b = 0.75 into the first equation (48 = a * 0.75) to solve for a:

48 = a * 0.75
48 / 0.75 = a
64 = a

Therefore, the exponential function represented by these points is:

y = 64 * 0.75^x