Acurve passes through the point (0,8) and has the property that the slope of the curve at every point p is three times the y-coordinate of p. what is the equation of the curve? y(x)=

solution:

slope is 3y

let one point is (x,y)

dy/dx = 3y

=> dy/y = 3dx

=> lny = 3x + c

substittue (0,8)

=> ln8 = c

so lny = 3x + ln8

=>ln(y/8) = 3x

=> y = 8e^(3x)

step-by-step explanation:

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