Function where the slope equals 10% of height?

[kitty08]

Hi,

I need help trying to find a function where the slope is exactly 10% of the height at all points. Any help would be great!!!

 

[daon2]

You mean derivative, I'm sure. f'(x)=0.1*f(x)? Well 0 certainly works. What other type of function do you know is proportional to its derivative?

 

[soroban]

Hello, kitty08!

Find a function where the slope is exactly 10% of the height at all points.

We have: .\(\displaystyle \dfrac{dy}{dx} \:=\:\dfrac{1}{10}y\)

Solve the differential equation.

 

[Deleted member 4993]

If

y = e^kx then

\(\displaystyle \frac{dy}{dx} \ = \ k * e^{kx} \ = \ k * y \)