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

f(x) = 4(3)x
f(x) = 4(x)3
f(x) = 6(3)x
f(x) = 6(x)3

The correct option is 1.

Step-by-step explanation:

If an exponential function passing through the point (2, 36), then the function satisfies by that point.

In option 1:

Substitute x=2,

Therefore option 1 is correct.

In option 2:

Substitute x=2,

Therefore option 2 is incorrect.

In option 3:

Substitute x=2,

Therefore option 3 is incorrect.

In option 4:

Substitute x=2,

Therefore option 4 is incorrect.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

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step-by-step explanation: