A curve passes through the point (0,7) and has the property that the slope of the curve at every point P is five times the y-coordinate of P

Question

A curve passes through the point (0,7) and has the property that the slope of the curve at every point P is five times the y-coordinate of P. What is the equation of the curve

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Thu Giang 4 years 2021-08-14T19:01:57+00:00 1 Answers 9 views 0

Answers ( )

  1. RuslanHeatt
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    2021-08-14T19:03:37+00:00
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    Answer:

    y(x) = 7e^(5x)

    Step-by-step explanation:

    The question says that the slope of the curve at every point P is five times the y-coordinate of P. This means that

    dy/dx = 5y

    Refer to solutions of differential equations, dy/dt = ky, being in the form of y(t) = y(0) e^(kt)

    Using the above stated law now, we can relate to our equation, saying that

    y(x) = y(0) e^(5x)

    The point given from the question is, (0, 7). This also means that y(0) = 7. So finally, we can have

    y(x) = 7e^(5x)

    And that is our needed equation of the curve

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