Question

So I am in a real pickle when it comes down to differential equations. I don't even know how to begin with these...

Answer 1

https://cdn.discordapp.com/attachments/182221549431029761/654834206530338816/Differential_Equations.png
@justjm can you help guide me in what I should be doing

Answer 2

So for problem 1195)

You need to use the differential equation \(y\left(t\right)=y_{o}e^{kt}\)
You know that the initial, \(y_{o}=3000\)
And that y(2) = 90,000

Thus

\(y(2)=3,000e^{2k}=90,000\)
Now you need to find k using your natural log rules and you get k=\(\frac{\ln\left(30\right)}{2}\). So you found your constant. Thus the final equation for part a is
\(y\left(t\right)=3000^{\left(\frac{\ln\left(30\right)}{2}\right)t}\)

part b.
Just find y(4)
part c.
Set y(t)=60,000 and find t using your ln rules.

Answer 3

I'm also just starting to do differential equations, so we just started today so I'm not sure if it's the right approach. But for the remainder of the problems, I think you just need to know which differential equation to use and then you're just plugging in, there isn't much calculus involved.

Answer 4

Anyhow for the next question, you're using the same differential equation from earlier
\(y\left(t\right)=y_{o}e^{kt}\)
They're giving you y initial as 50,000 and then you need to find k by plugging in y(30)=75000. Once you find k, you will have your differential. Now, plug y(t)=1000000 and find t.

Answer 5

We haven't learned how to deal with these today in class, and we're expected to do them for homework. Also, I believe we're literally being tested tomorrow on them after he explains how to do problems like these, so that was the reason I asked about it. Thanks for your input, but apparently the answer to the 1195a is 3000(30)^(t/2). I'll try to figure out what I can. Again, thanks for your help!

Answer 6

"You need to use the differential equation \(y(t)=y_oe^{kt}\)"

This is not a differential equation. The differential equation is \(\frac{dy}{dt}=ky\)

Answer 7

No problem, we started it yesterday but we're testing on it next semester and it's not on our semester exam.

And whoops, thank you @Zarkon , I wrote that without thinking. After all I only learned it like yesterday.

Answer 8

Oh and about the answer as \(3000\left(30\right)^{\frac{x}{2}}\), I believe it's the same as \(3000\left(e\right)^{1.7006x}\) but I used a different approach for it. You can derive it from each other.