Chapter 4 Section 3

\[ \definecolor{ucrblue}{rgb}{0.0627,0.3843,0.6039} \definecolor{ucrgold}{rgb}{0.9686,0.6941,0.2824} \definecolor{ucrred}{rgb}{0.8941,0,0.1686} \definecolor{ucrgreen}{rgb}{0.4706,0.7451,0.1255} \definecolor{ucraccent}{rgb}{1.0000,0.9569,0.8392} \DeclareMathOperator*{\LO}{O} \DeclareMathOperator*{\Lo}{o} \DeclareMathOperator*{\Recip}{Recip} \DeclareMathOperator*{\abs}{abs} \DeclareMathOperator{\pow}{pow} \]

Notes

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Linguistic Mapping Exercises

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Knowledge Checks

1. Graph the following function. Identify the domain, range, and asymptotes of \(f\). \[f(x)=-5^{x+1}+2.\]
2. Compute the following values.
   1. \(\log_3(243)\)
   2. \(\log_7\left(\frac{1}{49}\right)\)
   3. \(\ln\left(\frac{1}{e}\right)\)
   4. \(\log_\frac{1}{7}(343)\)
3. Graph the following function and identify the domain, range, and asymptotes of \(f\): \[f(x)=\log_\frac{1}{2}(-x-2)+2.\]
4. Solve the following equations.
   1. \(5^{x}-10=0\)
   2. \(4^{x}-\left(\frac{1}{16}\right)^{x+1}=0\)
   3. \(\log_3(-x-1)-\log_3(-x+12)=-2\)
5. Take \(a\) and \(b\) to be two real numbers so that \(\log_5(a)=5\) and \(\log_5(b)=-4.\) Compute the following.
   1. \(\log_5(25ab)\)
   2. \(\log_5(\frac{a^3}{5b^4})\)
6. A quantity \(A\) changes according to a linear model for change and \[\begin{cases} A(0)=4\\ A(1)=13.\end{cases}\] Identify a formula for \(A(t).\)
7. A quantity \(A\) changes according to an exponential model for change and \[\begin{cases} A(2)=10\\ A(5)=9. \end{cases}\] Identify a formula for \(A(t).\)
8. A mass of bacteria experiences exponential growth. At time \(3\) an experimenter has \(30\) grams of bacteria. At time \(7\), the mass has grown to a mass of \(50\).
   1. Determine the doubling time of the bacteria.
   2. Determine the time that it takes for the amount of the material to increase by a factor of \(3\).
   3. Determine the growth rate of the substance.

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Practice Problems

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