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exam _2a f08 - MAT 194 Name Test#2 Oct 31 2008 Show all...

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MAT 194 Name_________________________ Test #2 Oct. 31, 2008 Show all work! Answer all questions! (1) [9 pts] Solve the following equations exactly for x, if possible. If not, find an approximate solution (two decimal places). (a) 3×2 x - 2 = - 2 x + 5 (b) 3×2 5 x +3 = 7×6 x
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(2) [12 pts] There were 178 million licensed drivers in the US in 1989 and 187 million in 1999. Find a formula for the number, N , of licensed drivers in the US as a function of t , the number of years since 1989, assuming the growth is: (a) linear (b) exponential (c) Assuming exponential growth, when will the number of licensed drivers reach 200 million?
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(3) [10 pts] A very large pond has a population of frogs that grows exponentially. The pond begins with 15 frogs; six years later there are 270 frogs. (a) Give a formula for the population of frogs as a function of the time. (b) How long did it take for the population to double the first time? (c) What is the annual growth rate of this population of frogs?
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(4) [6 pts] Simplify each of the following expressions: (a) 100 log x (b) ln e ln e x (5) [10 pts] Simplify each of the following expressions: (a) x - 4 + 6 x - 8 1- 36 x - 8 3 xy - 7 x 2 y 6 x 2 - 11 x - 7 x 5 y 6
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