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elena55 [62]
3 years ago
7

A curve passes through the point (0, 5) and has the property that the slope of the curve at every point P is twice the y-coordin

ate of P. What is the equation of the curve? (Use x as the independent variable.)
Mathematics
1 answer:
Bess [88]3 years ago
5 0

Answer:

y =5e^{2x}

Step-by-step explanation:

Given that a curve passes through the point (0, 5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P.

Let y =f(x) be the equation of the curve

Since slope = 2y

we have

\frac{dy}{dx}= 2y\\\\y'     = 2dx\\ln y = 2x+C\\y = Ae^{2x}

To find A

It passes through (0,5)

Substitute x=0 and y=5

5=A

SO equation is

y =5e^{2x}

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