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MAT 151: College Algebra with Trigonometry

Subsection 0.3 Review of Exponential Functions and Logarithms Exercises

  1. Let \(g\) be as shown in Table 0.3.8.
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    Table 0.3.8.
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    \(x\) \(-2\) \(-1\) 0 1 2
    \(g(x)\) \(\frac{13}{9}\) \(\frac{13}{3}\) \(13\) \(39\) \(117\)
    1. Write a function equation for \(g\text{.}\)
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    2. Evaluate \(g(7)\text{.}\)
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    3. Solve \(g(x)=5000\text{.}\)
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    4. Write a function equation for \(g^{-1}\text{,}\) the inverse of \(g\text{.}\)
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    5. What are the domain and range of \(g\text{?}\)
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  2. Gaming PCs depreciate at a rate of 25% per year (after one year, the PC is worth only 75% of its value from the previous year).
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    1. If you purchase a new gaming PC for $1800, write a function equation to represent the value of the PC \(t\) years after you purchased it.
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    2. How much will the PC be worth after 5 years?
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    3. When will the PC be worth $100?
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  3. Osmium-182 (Os-182) has a half-life of 21.5 hours.
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    1. If you begin with a 10 gram sample of Os-182, write a function equation to represent the amount of Os-182 that will be present after \(t\) hours.
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    2. How many grams of Os-182 will be left after 12 hours?
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    3. How long will it take until there is only 1 gram of Os-182 remaining.
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  4. Simplify each expression below. Assume all variables represent non-negative real numbers. Write your answers using only positive exponents.
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    1. \(\displaystyle \displaystyle \frac{x^4y^{-4}}{3x^{-2}y^{-4}}\)
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    2. \(\displaystyle \displaystyle (3y^{-1}z^4)^2\)
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    3. \(\displaystyle \displaystyle (x^{-4}z^4)^{-4}\)
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    4. \(\displaystyle \displaystyle \left( \frac{m^{-4}n^6}{m^{-2}n^6} \right)^4\)
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    5. \(\displaystyle \displaystyle \frac{(y^6)^{-6}}{(y^{-6})^{-4}}\)
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    6. \(\displaystyle \displaystyle (-4x^2y^{-2}z)(3xy^2z^{-3})\)
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    7. \(\displaystyle \displaystyle \sqrt{150x^2y^5z^3}\)
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    8. \(\displaystyle \displaystyle \sqrt[3]{8a^6b^{-9}c^2}\)
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    9. \(\displaystyle \displaystyle -\sqrt{10x^2} \cdot \sqrt{6x}\)
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