#### 3rd Midterm

#### Spring 1998

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1. Graph y = 2^{x}

2. Change to logarithmic
form b^{x} = a

3. Change to exponential
form t = ln x

4. Expand

5. Express as a single log
log x - 2 log y + 3 log z

6. Solve for
x and check

log_{5} (x + 3) + log_{5} (x-1) = 1
7. Suppose that the
population of a city is 30,000 in 1985 and 50,000 in 1995. Assume
further that the population is given by the formula

A = Pe^{rt}
where P is the population in the year 1985, t is the number of
years since 1985, A is the population t years after 1985, and r is a
suitable constant.

- a) Find the value of r
which will explain this data.
- b) Use this value of r
to predict the population in the year 2000
- c) With this value of
r, in what year will the population double from the 1985
population?

8. Write out Pascal's
triangle down to the 7th row.

9. Remove parentheses and
simplify (x + y)^{5}

10. Compute
_{25}C_{5}

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