If f'(x) = 3*f(x) for all x, and f(0) = 10, what is f(2)?

Question

If f'(x) = 3*f(x) for all x, and f(0) = 10, what is f(2)?

Answer 1

Hi Christopher,

 

Here us a way to think about this.

 

dy/dx = 3y

 

dy/y = 3dx  (now integrate both sides)

 

ln|y| = 3x + c

 

y = e^(3x+c) (put in exponential form)

 

y = e^c e^3x  

 

y = Ae^3x (e^c is an arbitrary constant)

 

Use the condition that f(0) = 10 to find the particular solution, i.e. the value for A.

 

y = 10e^3x  or f(x) = 10e^3x

 

So, f(2) = 10e⁶