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Chapter 3: Problem 74
Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. $$\log _{16} 57.2$$
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One problem with all exponential growth models is that nothing can grow exponentially forever. Describe factors that might limit the size of a population.
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The functions \(f(x)=\left(\frac{1}{3}\right)^{x}\) and \(g(x)=3^{-x}\) have the same graph.
Graph each of the following functions in the same viewing rectangle and then place the functions in order from the one that increases most slowly to the one that increases most rapidly. $$y=x, y=\sqrt{x}, y=e^{x}, y=\ln x, y=x^{x}, y=x^{2}$$
a. Evaluate: \(\log _{2} 16\) b. Evaluate: \(\log _{2} 32-\log _{2} 2\) c. What can you conclude about \(\log _{2} 16,\) or \(\log _{2}\left(\frac{32}{2}\right) ?\)
Use a calculator with \(a\left[y^{x}\right]\) key or \(a \square\) key to solve. India is currently one of the world's fastest-growing countries. By \(2040,\) the population of India will be larger than the population of China; by \(2050,\) nearly one-third of the world's population will live in these two countries alone. The exponential function \(f(x)=574(1.026)^{x}\) models the population of India, \(f(x),\) in millions, \(x\) years after 1974 a. Substitute 0 for \(x\) and, without using a calculator, find India's population in 1974 b. Substitute 27 for \(x\) and use your calculator to find India's population, to the nearest million, in the year 2001 as modeled by this function. c. Find India's population, to the nearest million, in the year 2028 as predicted by this function. d. Find India's population, to the nearest million, in the year 2055 as predicted by this function. e. What appears to be happening to India's population every 27 years?
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