Thursday

January 29, 2015

January 29, 2015

Posted by **sarah** on Friday, February 25, 2011 at 4:29pm.

- elementary calc -
**Reiny**, Friday, February 25, 2011 at 5:11pmWhen a derivative of a function is a multiple of the y value of the function, it suggests an exponential function.

let the function be y = a e^(kx), where a and k are constanst

dy/dx = ak e^(kx)

given ak e^(kx) = 3y = 3(a e^(kx))

then ak = 3a

k = 3

so we know y = a e^(3x)

at (0,2)

2 = a e^(0)

a = 2

then y = 2 e^(3x)

then dy/dx = 6 e^(3x)

when x=1

dy/dx = 6 e^3

- elementary calc -
**Damon**, Friday, February 25, 2011 at 5:14pmdy/dx = 3 y

dy/y = 3 dx

ln y = 3 x + c

y = C e^3x

if x = 0, y = 2

so

y = 2 e^3x

when x = 1

y = 2 e^3 = 40

dy/dx = 3y = 120

**Answer this Question**

**Related Questions**

calculus - the graph of f(x) passes through the point (0,6). the slope of f at ...

calculus - The graph of f(x) passes through the point (0,3) . The slope of f at...

math - i have more than one question so if u no any of the answers please tell ...

Calc - Find a parabola with the equation y=ax^2+bx+c and has slope 4 at x=1, ...

Calculus Help Please!!! Check - A curve passes through the point (0, 2) and has...

Math/Algebra do u know how to do slope intercept? - The following problems are ...

math - I have a few question so I will number them off. Please answer them for ...

Calculus - So here is the question: Find and equation of the tangent line to the...

Algebra2 - Write an equation for the line in point/slope form and slope/...

calc - The slope of the tangent to the curve y=f(x) is given by (1/9)(x^2)(y^2...