Question

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

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

Answer 1

The equation that represents an exponential function passing through the point (2, 36) is Option A: f(x) = 4(3)^x. This is determined by substituting the x-value into each given function and finding the corresponding y-value that matches the point.

Step-by-step explanation:

To find which equation represents an exponential function that passes through the point (2, 36), we need to substitute the x-value of the point into each function and determine which one provides the corresponding y-value. An exponential function is of the form f(x) = a(b)^x, where a is the initial value and b is the base of the exponential function that indicates the factor of growth or decay.

Let's try each option and evaluate when x = 2:

• Option A: f(x)=4(3)x, f(2)=4(3)2 = 4(9) = 36 (This matches the point (2, 36))
• Option B: f(x)=4(x), f(2)=4(2) = 8 (This does not match the point)
• Option C: f(x)=6(3)x, f(2)=6(3)2 = 6(9) = 54 (This does not match the point)
• Option D: f(x)=6(x), f(2)=6(2) = 12 (This does not match the point)

The only function that passes through the point (2, 36) is the one found in Option A: f(x) = 4(3)x.