Find the formula for an exponential function that passes through the two points given. (x, y) = (0, 4) and (x, y) = (3, 32)

Given:

The exponential function passes through two points (0,4) and (3,32).

To find:

The formula for the exponential function.

Solution:

The general form of an exponential function is

         ...(i)

where, a is initial value and b is growth factor.

The exponential function passes through two points (0,4) and (3,32). It means the function must be satisfy by these points.

Putting x=0 and y=4 in (i), we get

Putting a=4, x=3 and y=32 in (ii), we get

Divide both sides by 4.

Taking cube root on both sides.

Putting a=4 and b=2 in (i), we get

Therefore, the required formula for the exponential function is .

this is not the answer this is just a question. is this middle school math?

step-by-step explanation:

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