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Chapter 4: Problem 28
Evaluate each expression without using a calculator. $$\log _{7} 49$$
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The value \(c\) in the logistic function \(f(x)=\frac{\epsilon}{1+a c^{-2}}\) is sometimes called the carrying capacity. Can you give a reason why this term is used?
The value of a 2003 Toyota Corolla is given by the function $$v(t)=14,000(0.93)^{t}$$ where \(t\) is the number of years since its purchase and \(v(t)\) is its value in dollars. (Source: Kelley Blue Book) (a) What was the Corolla's initial purchase price? (b) What percent of its value does the Toyota Corolla lose each year? (c) How long will it take for the value of the Toyota Corolla to reach \(\$ 12,000 \)
Applications In this set of exercises, you will use inverse functions to study real-world problems. A woman's dress size in the United States can be converted to a woman's dress size in France by using the function \(f(s)=s+30,\) where \(s\) takes on all even values from 2 to \(24,\) inclusive. (Source: www.onlineconversion \(. \operatorname{com})\) (a) What is the range of \(f ?\) (b) Find the inverse of \(f\) and interpret it.
Solve the logarithmic equation and eliminate any extraneous solutions. If there are no solutions, so state. $$\log (2 x+5)+\log (x+1)=1$$
The 1960 earthquake in Chile registered 9.5 on the Richter scale. Find the energy \(E\) (in Ergs) released by using the following model, which relates the energy in Ergs to the magnitude \(R\) of an earthquake. (Source: National Earthquake Information Center, U.S. Geological Survey) $$\log E=11.4+(1.5) R$$
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