Question

Which equation represents an exponential function that passes through the point (2, 36)?

A. f(x) = 4(3)x
B. f(x) = 4(x)3
C. f(x) = 6(3)x
D. f(x) = 6(x)3

Answer 1

The correct equation is A.

Explanation:

To determine which equation represents an exponential function that passes through the point (2, 36), we can substitute the x-value (2) and y-value (36) into each equation and see which equation satisfies the given point.

Let's evaluate each equation:

A. f(x) = 4(3)^ x

Substituting x = 2: f(2) = 4(3)^2 = 4(9) = 36

B. f(x) = 4(x)^3

Substituting x = 2: f(2) = 4(2)^3 = 4(8) = 32

C. f(x) = 6(3)^ x

Substituting x = 2: f(2) = 6(3)^2 = 6(9) = 54

D. f(x) = 6(x)^3

Substituting x = 2: f(2) = 6(2)^3 = 6(8) = 48

Only option A, f(x) = 4(3)^ x, satisfies the condition, as it yields f(2) = 36. Therefore, the correct equation is A.