PRACTICE Exam #2

Instructor: Eric Harshbarger

Student Name: ____________________________

Student ID #: ______________________

Show all relevant work (use back of pages for scratch paper, if needed). CIRCLE FINAL ANSWERS.

1. [3 pts each] Evaluate each expression; write answer as a single complex number of the form a + bi.

a)

5−3 i 42 i

b)

7−2i−9−3 i

c)

8−3 i126i

d)

3−−4 6− −5

e)

4−i

75i

2. [4 pts each] Find all solutions of each equation and express them in the form a + bi.

a)

x2 - 3x + 3 = 0

b)

4x2 - 16x + 19 = 0

3. [3 pts each] Use a calculator to evaluate the function f(x) = 5·2x for the given input values of x.

Express your answer rounded to three decimal places.

a)

f 6.1 =

b)

f 3 =

c)

f −0.4 =

4. [3 pts each] Find the exact value (do not use a calculator or decimal places) of each expression:

a)

log63 + log612

b)

log32 - log354

c)

ln e4

5. [4 pts each] Combine each expression into a single logarithm and simplify, if possible:

a)

b)

log7(x2 - 5x + 6) - log7(x - 3)

ln 2ln x1−4 ln 3 x7

6. [4 pts] Use a calculator to evaluate this logarithm, rounded to three decimal places: log7168

7. [10 pts] For g(x) = 2x, complete the chart below: x g(x)

3

2

1

0

-1

-2

-3

8. [4 pts] Plot the points and sketch the graph of g from #7 above using the chart as a guide.

9. [4 pts] Now, on the same grid above, sketch the graph of h x =4−2 x2

10. [3 pts each] Find the solution to each equation; you may leave the answer in exact form, or rounded to three decimal places:

a)

3 x2=17

b)

e 3−5 x =16

11. [4 pts each] In each equation, solve for x; you may leave the answer in exact form, or rounded to three decimal places:

a)

b)

e 4 x 2 e 2 x −15=0

log3(x + 15) - log3(x - 1) = 2

12. [10 pts] A sum of $1000 is invested at an interest rate of 7% per year. Find the