Keira S.

asked • 06/22/21

Reimann Sums and FTC

A “Big Rig,” or eighteen wheeler truck will burn diesel at a rate of  G to the power of apostrophe left parenthesis t right parenthesis equals 17 minus e to the power of negative t end exponent  gallons each hour, t hours after a fill-up.


Find the number of gallons of gas consumed by a typical “Big Rig” 10 hours after a fill-up. 

The number of gallons of gas consumed is

Keira S.

In case the link is broken, the equation is G'(t)=17-e^-t
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06/22/21

Andrew D.

tutor
The trick to answering this kind of question is to make sure that you understand the tools you need to use. That is, you'll have to conceptualize the question so that you can set up your equations correctly. The differential equation that is given represents the changing rate of diesel consumption. So, then it would follow that G(t) is the equation representing the amount of gas consumed at time t. Thus, the question requires that you solve the ODE [assuming that G(0)=0] and then integrate G(t) from t=0 to t=10. Of course, since this is labeled "Riemann Sums," it implies that you are finding an approximation rather than an exact analytical answer. The only issue is that there is no time step given nor is it specified whether you are meant to find the left, right, or midpoint Riemann sum. So, if this is for an assignment or test, I'm not entirely certain how you would make the assumptions needed for an automated grading system, for example, to mark it correct.
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06/22/21

1 Expert Answer

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Bradford T. answered • 06/22/21

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Since the title is marked Riemann Sums and FTC (Fundamental Theorem of Calculus), I think you can use the FTC or just integrate to get your answer:


G(t) = ∫ab G'(t) dt


For this case G(t) = ∫010 17-e-t dt


I guess theoretically you could do a Riemann sum if you let Δx = 10/n and go with some closed form for

e-(10i/n). Then take the limit n→∞


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Keira S.

I did the problem and I received 169. Is this answer correct?
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06/23/21

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