Unformatted text preview: nterval (10 ln(3), ∞).
Our sign diagram is below, and next to it is our graph of t = T (t) from Example 6.1.2 with the
horizontal line y = 100.
0 0 (−)
10 ln(3) 120 y = 100 80
60 H.A. y = 70 40
2 4 6 8 10 12 14 16 18 20 t y = T (t) In order to interpret what this means in the context of the real world, we need a reasonable
approximation of the number 10 ln(3) ≈ 10.986. This means it takes approximately 11 minutes for
the coﬀee to cool to 100◦ F. Until then, the coﬀee is warmer than that.8
We close this section by ﬁnding the inverse of a function which is a composition of a rational
function with an exponential function.
is one-to-one. Find a formula for f −1 (x) and check
ex + 1
your answer graphically using your calculator.
Solution. We start by writing y = f (x), and interchange the roles of x and y . To solve for y , we
ﬁrst clear denominators and then isolate the exponential function. Example 6.3.4. The function f (x) = 8 Critics may point out that since we needed to use the calculator to interpret our a...
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