Which exponential function goes through the points (1, 16) and (4, 128)?
f(x) = 4(4)^x
f(x) = 8(2)^x
f(x) = 8(2)^-x
f(x) = 4(4)^-x

Solution:

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

If it passes through the points, then the points should satisfy the equation. Let us check each option given.

1. f(x) = 4(4)^x: (1, 16) and (4, 128)

16 = 4(4)

16 = 16

point 1 lies on it

128 = 4(4)⁴

128 ≠ 1024

Point 2 doesn’t lie on it

2. f(x) = 8(2)^x: (1, 16) and (4, 128)

16 = 8(2)

16 = 16

Point 1 lies on it

128 = 8(2)⁴

128 = 128

Point 2 lies on it

Hence, the required equation is f(x) = 8(2)^x

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

Summary:

The f(x) = 8(2)^x exponential function goes through the points (1, 16) and (4, 128).