Chapter 4 Section 3

Notes

Linguistic Mapping Exercises

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.

Practice Problems

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