Form a differential equation if y=ae^-4x+be^-6x

Assuming A and B are constants, the trick for forming a differential equation when the original equation contains e is to keep each term the same and multiply by the derivative of the exponent.

For example, if your original function is y = Aeˣ + Beˣ, then the derivative, y', would be: y' = (Aeˣ)*x' + (Beˣ)*x'.

Therefore, for your equation, y' = -4Ae⁻⁴ˣ + -6Be⁻⁶ˣ.

Hope this helps!

First we have to find the slope of the linear equation, slope=m=(y2-y1)/(x2-x1)

m=(10,400-4,200)/(2015-2007)=6200/8=775 so we so far have a line of:

s=775(y-2003)+b, using either original point we can solve for b, the y-intercept which is the initial value as well...I'll use point (2007, 4200) and we get:

4200=775(2007-2003)+b

4200=3100+b

b=$1100

s(y)=775(y-2003)+1100

Maggie initially deposited $1,100. Hope this helps!