Question

The table represents some points on the graph of an exponential function.
X:1,2,3,4
f(x):48,36,27,20.25

Answer 1

To find the equation of the exponential function represented by these points, we can first look at the pattern in the values of f(x) as x increases.

The general form of an exponential function is f(x) = a*b^x, where "a" is the initial value (when x = 0) and "b" is the base of the exponential function.

Using the points provided:

When x = 1, f(1) = 48, so 48 = a*b^1
When x = 2, f(2) = 36, so 36 = a*b^2
When x = 3, f(3) = 27, so 27 = a*b^3
When x = 4, f(4) = 20.25, so 20.25 = a*b^4

We can now set up a system of equations to solve for "a" and "b":

48 = a*b
36 = ab^2
27 = ab^3
20.25 = ab^4

Dividing the equations:

(48/36) = b
(36/27) = b
(27/20.25) = b

From the above calculations, we find that b = 4/3.

Substituting back into the first equation:

48 = a*(4/3)
48 = 4a/3
a = 48*3/4
a = 36

Therefore, the equation of the exponential function represented by the points is:

f(x) = 36*(4/3)^x