Question

Help with rate of change!

Answer 1

Any specific question?

Answer 2

hold on let me put an attachment

Answer 3

I'm assuming you only need help with the second problem. In that case, the rate of change of \(s(n)\) is given by either the average rate of change or derivative, depending on whether you want the instantaneous rate of change or not. Seeing as the question is asking for the r.o.c. at \(n=5\), it looks like it wants the instantaneous r.o.c.
\[s(n)=400-100e^{-1/2~n}\]
The inst. r.o.c. at \(n=5\) is given by the derivative of \(s(n)\) at \(n=5\), or \(s'(5)\).
\[s'(n)=-\frac{1}{2}(-100)e^{-1/2~n}\\
s'(n)=50e^{-1/2~n}\]
Plug in \(n=5\):
\[s'(5)=50e^{-5/2}\approx\cdots\]

Answer 4

I dont understand

Answer 5

you need to find s'
and evaluate s' at n=5

Answer 6

how do i do that? can you show me step by step so i can follow

Answer 7

what is the derivative of 400?

Answer 8

what is the derivative of e^(-.5n)? hint use chain rule

Answer 9

i dont know, i so lost

Answer 10

you must know the derivative of a constant?