Question

Which exponential function goes through the points (1,16) and (4,128)?

A. f(x) = 4(4)x.
B. f(x) = 8(2)x.
C. f(x) = 8(2)x.
D. f(x) = 4(4).

Answer 1

To determine the exponential function that goes through the points (1,16) and (4,128), we can use the general form of an exponential function and substitute the coordinates of the points into the function.

Step-by-step explanation:

The exponential function that goes through the points (1,16) and (4,128) can be determined using the general form of an exponential function: f(x) = a(b)^x. To find the values of 'a' and 'b', we substitute the coordinates of the given points into the function.

For the first point (1,16):

• 16 = a(b)^1

For the second point (4,128):

• 128 = a(b)^4

By solving these two equations simultaneously, we can find the values of 'a' and 'b' which will give us the exponential function that passes through both points.