A curve passes through a point P(0, 3) and has the property that slope of curve at every point P is twice the y-coordinate of point P. Use the concept of exponential growth function to find the equation of curve.

The equation of curve is .

Step-by-step explanation:

The exponential growth function is represented by the expression described below:

(1)

Where:

- Independent variable.

- Dependent variable.

- Initial value of .

- Base.

By deriving (1), we obtain an expression for the slope of the curve:

(2)

If we know that , and , then we have the following system of equations:

(3)

(4)

By (3) in (4):

Therefore, the equation of curve is .

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