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**Solve the equation. Give an exact solution.**

1) ln x - ln(x - 2) = 1 1)

2) log(x + 10) - log(x + 4) = 2 2)

**Solve the problem.**

3) In the formula A(t) = A0ekt, A is the amount of radioactive material remaining from an

initial amount A0 at a given time t, and k is a negative constant determined by the nature of the material. An artifact is discovered at a certain site. If it has 57% of the carbon-14 it originally contained, what is the approximate age of the artifact? Carbon-14 decays at the rate of 0.0125% annually. Round to the nearest year, if necessary.

4) A certain radioactive isotope has a half-life of approximately 1050 years. How many years to the nearest year would be required for a given amount of this isotope to decay to 45% of that amount?

5) Several years ago, a large city undertook a major effort to encourage carpooling in order to reduce traffic congestion. The accompanying table shows the number of carpoolers, in thousands, from 2007 to 2012. Use regression to obtain a function f(x) = a + b ln x that models the data, where x = 1 corresponds to 2007, x = 2 to 2008, and so on. Round the constants a and b to the nearest hundredth. Year 2007 2008 2009 2010 2011 2012 Carpoolers 3.9 8.1 10.3 11.8 12.6 13.2

Subject | Mathematics |

Due By (Pacific Time) | 12/04/2013 08:00 pm |

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