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Chapter 3: Problem 87
After a \(60 \%\) price reduction, you purchase a computer for \(\$ 440 .\) What was the computer's price before the reduction? (Section P.8, Example 4)
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Solve and graph the solution set on a number line: \(2 x^{2}+5 x<12 .\)
Use Newton's Law of Cooling, \(T=C+\left(T_{0}-C\right) e^{k t},\) to solve this exercise. At 9: 00 A.M., a coroner arrived at the home of a person who had died. The temperature of the room was \(70^{\circ} \mathrm{F}\), and at the time of death the person had a body temperature of \(98.6^{\circ} \mathrm{F} .\) The coroner took the body's temperature at 9: 30 A.M., at which time it was \(85.6^{\circ} \mathrm{F},\) and again at 10: 00 A.M., when it was \(82.7^{\circ} \mathrm{F} .\) At what time did the person die?
Explain how to solve an exponential equation when both sides cannot be written as a power of the same base. Use \(3^{x}=140\) in your explanation.
Use a calculator with an \(\left[e^{x}\right]\) key to solve. The bar graph shows the percentage of U.S. high school seniors who applied to more than three colleges for selected years from 1980 through 2013. (BAR GRAPH CAN'T COPY) The data can be modeled by $$ f(x)=x+31 \text { and } g(x)=32.7 e^{0.0217 x} $$ in which \(f(x)\) and \(g(x)\) represent the percentage of high school seniors who applied to more than three colleges \(x\) years after 1980\. Use these functions to solve . Where necessary, round answers to the nearest percent. In college, we study large volumes of information \(-\) information that, unfortunately, we do not often retain for very long. The function $$ f(x)=80 e^{-0.5 x}+20 $$ describes the percentage of information, \(f(x),\) that a particular person remembers \(x\) weeks after learning the information. a. Substitute 0 for \(x\) and, without using a calculator, find the percentage of information remembered at the moment it is first learned. b. Substitute 1 for \(x\) and find the percentage of information that is remembered after 1 week. c. Find the percentage of information that is remembered after 4 weeks. d. Find the percentage of information that is remembered after one year (52 weeks).
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(\log _{b} x\) is the exponent to which \(b\) must be raised to obtain \(x\).
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