The problem I am having with this is that I learned how to solve this type of problem a long time ago and when I was taught it they used another type of formula with different letters so I am kind of lost: (Can you tell me what I got write and what I did wrong if the answer is incorrect-Thanks)

Here is the question:

I am given the equation dA/dt=-kA

A(t) = the amount of material present(in grams)

t = time (minutes)

k= some positive constant

a.) Derive an equation for the amount A(t) present at time t in terms of the constant k and the amount A(0) present at time t=0

This is what I did: (However I used the letters I learned and so would this be correct)

(- dN/N)= λ * dt

So,

dN(t)/dt =-λ N(t)

dN(t)/N(t)= -λ dt

In N(t)=-λ dt

In N(t)= -λ t+C

N(t)=e^C e^-λt= Noe^-λ t (the o is between the N and e but on the bottom)

(did I do the problem correctly- if not what steps am I missing - Thanks)

b.) If A(5)= 1/3 A(3), find k

(What would I do to find the solution to this problem- could you tell me the steps/formula to take- Thanks)

c.) At what time t will the amount A(t) be 1/4 A(0)

(Could you help me with this problem as well I don't now where ton start- could you show me the steps to take- Thanks)

Thank you for all the help I really appreciate it