# Math Help - Antidervatives?

1. ## Antidervatives?

My lecturer give weekly assignments for our class and each assignment is individual, he also makes a sample sheet with similar questions that we may ask for assistance with tutors and the likes, There's one particular question that has me stumped in my assignment I'm aware that anti derivatives are key to solving the question but I can't figure out how to go about solving it.
This is the sample sheets version of the question so I'm more interested in the step by step solution than the actual answer. Thanks in advance!

And just so I can't be accused of trying to get people to do my assignment here's a link to assignment page log in as a guest and choose sheet 6 and you'll see the question there.
http://alberti.nuigalway.ie:8125/exquery.html

2. ## Re: Antidervatives?

Originally Posted by Daithi19
My lecturer give weekly assignments for our class and each assignment is individual, he also makes a sample sheet with similar questions that we may ask for assistance with tutors and the likes, There's one particular question that has me stumped in my assignment I'm aware that anti derivatives are key to solving the question but I can't figure out how to go about solving it.
This is the sample sheets version of the question so I'm more interested in the step by step solution than the actual answer. Thanks in advance!

And just so I can't be accused of trying to get people to do my assignment here's a link to assignment page log in as a guest and choose sheet 6 and you'll see the question there.
http://alberti.nuigalway.ie:8125/exquery.html
Since they have given you the growth rate and a formula for it, just plug and chug.

$r=\frac{1}{N}\frac{dN}{dt} \iff .06dt=\frac{dN}{N}$

Now just integrate both sides of the equation and use the fact that $N(0)=3 \times 10^9$

post back if you get stuck!

3. ## Re: Antidervatives?

This problem really has me stuck I'm still not sure how to do it, would you mind doing the problem step by step and explaining each step as you go?

4. ## Re: Antidervatives?

Originally Posted by Daithi19
This problem really has me stuck I'm still not sure how to do it, would you mind doing the problem step by step and explaining each step as you go?
You have been told the differenbtial equation to solve:

$0.6N = \frac{dN}{dt}$

and you have been told that it's seperable:

$0.6 dt = \frac{1}{N} dN$.

And you have been told what to do with it: Integrate both sides.

Surely you have made some progress. Show what you have done and say where you are stuck.

5. ## Re: Antidervatives?

All right so I integrate
$0.6 dt = \frac{1}{N} dN$
and I end up with
$0.6 t = log (N)$
But I'm not sure where to go from here, do I sub in 35 for t?
If I do that I end up with N= 1318815734 but that's obviously wrong so I'm still unsure of what to do.

6. ## Re: Antidervatives?

Originally Posted by Daithi19
All right so I integrate
$0.6 dt = \frac{1}{N} dN$
and I end up with
$0.6 t = log (N)$
But I'm not sure where to go from here, do I sub in 35 for t?
If I do that I end up with N= 1318815734 but that's obviously wrong so I'm still unsure of what to do.
First, the antiderivative of \displaystyle \begin{align*} \frac{1}{x}\,dx \end{align*} is not \displaystyle \begin{align*} \ln{x} \end{align*}, it's \displaystyle \begin{align*} \ln{|x|} \end{align*}.

Second, you have forgotten your integration constant.

You have been given a point that satisfies the solution to your DE, use it to evaluate the constant.