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**Unformatted text preview: **termine the value of i as t → ∞. (This is called the steady
state current.)
12. If the voltage in the circuit in Exercise 11 above is switched oﬀ after 30 seconds, the current
is given by the piecewise-deﬁned function i(t) =
22 2 − 2e−10t if 0 ≤ t < 30
2 − 2e−300 e−10t+300 if t ≥ 30 This roast was enjoyed by Jeﬀ and his family on June 10, 2009. This is real data, folks! 6.5 Applications of Exponential and Logarithmic Functions 393 With the help of your calculator, graph y = i(t) and discuss with your classmates the physical
signiﬁcance of the two parts of the graph 0 ≤ t < 30 and t ≥ 30.
13. In Exercise 7 in Section 2.3, we stated that the cable of a suspension bridge formed a parabola
but that a free hanging cable did not. A free hanging cable forms a catenary and its basic
ex + e−x
shape is given by y =
. Use your calculator to graph this function. What are its
2
domain and range? What is its end behavior? Is it invertible? How do you think it is related
to the function given in Exercise 5 in Section 6.3 and the one given in the answer to Exercise 7
in Section 6.4? When ﬂipped upside down, the catenary makes an arch. I...

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