chain rule - calculus

Question

The electric potential in a circuit is given by

V(t) = 320e^−3.1t

where t is measured in seconds and V is measured in volts. Answer the following, with correct units.

When is the potential equal to 150 volts? Be accurate to 4 decimal places.

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How fast is V changing at that instant in time? Be accurate to one decimal place.

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When is the voltage changing at− 50 volts per second? Be accurate to 4 decimal places.

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Answer 1

So Roz A.,

Since your first question is just plug in the voltage given and solve for t, you have to become acquainted with the inverse function of the exponential function (e^x). What is the inverse function? If you don't know that yet, you probably need some one-on-one tutoring for that, before you start taking first derivatives of the voltage with respect to time (dV/dt).

But let's assume that suddenly you remember the ln(x) function and can actually apply it to part (a).

So then, for (b), derive the dV/dt function, i.e. V ' (t). You just have to plug the value of t from part (a) into that V ' (t) equation and crank out the answer, for (b).

Then, you have the general equation for V '(t). So put the -50 value in for V '(t) and solve the expression for (t), that will be the answer for (c).

Please remember to carry plenty of precision (2 more digits than for the eventual answers) throughout, and only round the final answers once you have them accurately calculated. Do not, in contrast, take a rounded answer from (a) and use it for calculations in (b). That would be like saying, "because the train only comes through this crossing for 5 minutes per day, I'm perfectly safe driving through without ever looking at the crossing lights and gate bar." Sometimes that works, and sometimes not.

-- Cheers, --Mr. d.