Concept explainers
Illustrative Applications Exercises
Moore’s Law According to Moore’s law, the number of transistors on a computer chip doubles about every
a. Use the common logarithm to solve the equation
b. Use the laws of exponents to show that an exponential function with yearly growth factor
c. Explain using part b why Moore’s law says that every year the number of transistors on a computer chip increases by a factor of
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Chapter 4 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Given a formula for an exponential function, is itpossible to determine whether the function grows ordecays exponentiallyjust by looking at the formula?Explain.arrow_forwardBy finding the appropriate logarithmic or exponential form of the equation, as in Example 1.arrow_forwardRewrite e3.5=h as an equivalent logarithmicequation.arrow_forward
- Rewrite 163x5=1000 as a logarithm. Then applythe change of base formula to solve for x using thenatural log. Round to the nearest thousandth.arrow_forwardRecall the formula for continually compoundinginterest, y=Aekt. Use the definition of a logarithmalong with Properties of logarithms to solve theformula for time t such that tis equal to a singlelogarithm.arrow_forwardRewrite 512x17=125 as a logarithm.Then applythe change ofbase formula to solve for x using thecommon log. Round to the nearest thousandth.arrow_forward
- Discuss the meaning of the common logarithm.What is its relationship to a logarithm with base b,and how does the notation differ?arrow_forwardRecall the compound interest formula A=a(1+rk)kt. Use the definition of a logarithm along withproperties of logarithms to solve the formula for time t.arrow_forwardUse the Change of Base Formula and a calculator to evaluate the logarithm, rounded to six decimal places. Use either natural or common logarithms. log122.5arrow_forward
- Use a calculator to help solve each problem. Tritium decay Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 50 grams, how much remain after 100 years?arrow_forwardSolve: 3logx=log64arrow_forwardUse logarithms to find the exact solution for 3e6n2+1=60. If there is no solution, write nosolution.arrow_forward
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