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anonymous
 5 years ago
Oil is leaking from a tanker at the rate of R(t) = 2000e^(0.2t) gallons per hour where t is measured in hours. How much oil leaks out of the tanker from the time t = 0 to t = 10
anonymous
 5 years ago
Oil is leaking from a tanker at the rate of R(t) = 2000e^(0.2t) gallons per hour where t is measured in hours. How much oil leaks out of the tanker from the time t = 0 to t = 10

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0For background knowledge, what math are you in?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay, that's what I thought. So you know integrals?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Do you know what they're used for?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well, this is one prime example of what they're used for. If you graphed the equation you said, taking the integral of it would essentially find the area filled in between your line and the x axis

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What this means when the line represents a rate is that your x axis will essentially represent time elapsed and the area filled in is the total

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah, I think so! Can I just plug the equation into the calculator to graph it and then get my answer from there?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Not really (unless you know have a TI89 which can integrate)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hahaha. Well if you're allowed to, go for it. Before I say do it to it, how would you set up the integral for this equation?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Also, just thought you should know that sunflowers are my dad's favorite so I approve of the name, haha

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{10}2000e^(.2t)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Haha well they're my favorite too X)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You have to include dt, but yea.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oops! Ok! Then I get confused though, where do I go from there?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Once you take the integral from 010 of a rate equation, you've found the total. What I mean by that is this. Let's say you're going to the beach at a rate of 63 miles per hour from the first hour to the fourth hour

bahrom7893
 5 years ago
Best ResponseYou've already chosen the best response.0let u be 0.2t, du = .2dt and integrate...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeaaah.... You lost me. I don't understand how to take the integral, the fact that theres an e there messes me up.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I thought you just put the integral into your calculator. That should be your answer.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I was just about to explain why that's the answer.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0That seems too easy though, aren't there more steps or something?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0That's it, gimme a sec to explain.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Like I was saying, I drive at 63 miles/hour from the first hour to the fourth (not including). I want the total number of miles driven. Using an integral to do this, I set it up like this:

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{1}^{4} (63 miles/hour)dhour\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The 1 and 4 are points 1 and 4 on the hour axis (x axis in your calculator)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Integrating with respect to dhour essentially gets rid of the /hour and returns just the total number of miles driven.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Go ahead and test it to make sure.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0That integral should return the same number as if you just did the simple multiplying of 3 hours by the 63 miles/hour

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0While it's seemingly more work to do it with something simple like my example, it translates exactly the same way as in your example.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok! I think that makes sense! Can you check my answer to my problem though? I'm getting 8647 gallons when I use the calculator.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If you're given a rate with a time variable, you just take an integral that starts at the first point and ends at the last point and integrate the rate with respect to the time variable, in this case t.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay, lemme load it up

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Close enough :) I don't know why expected that to be so much more complicated, thank you!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yea, it's not that bad when you understand what integrals really do.
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