math help

MTH 107 Section -- EXAM #4 Part 2 NAME:

DATE:

HONOR CODE: On my honor, I have neither given nor received any aid on this examination.

Signature:

SHOW ALL WORK ON THIS EXAM!!!

1. Solve: )8(log)1(log)4(log

444 +=++− xxx

2. Ed invests $10,000 in a certificate of deposit earning 2.5% interest.

a) If interest is compounded continuously, how much will he earn after 3 years?

Recall: rt

PeA =

b) How long will it take for Ed to earn $30,000?

c) What is the effective simple interest rate for this account?

3. Solve the system of linear equations: 2𝑥 − 2𝑦 = 10

−21𝑥 + 21𝑦 = 14

4. Solve: 4𝑥 − 10 ∗ 4−𝑥 = 3

5. a) Show me that 𝑓(𝑥) = |𝑥| is not 1-1 b) Show me that 𝑓(𝑥) = 𝑥3 is 1-1

6. Solve the system of non-linear equations:

4𝑥2 + 3𝑦2 = 4 4𝑥2 − 12𝑦2 = −6

7. Let the function g be defined as follows: 3 2

4

18 )(

+ =

x xg

Express g as a composition of four functions. What is its domain?

Bonus (5 Points):

Solve the system of equations: 1

𝑥 + 1

𝑦 = 8

3

𝑥 − 5

𝑦 = 0

Hint: We did not go over this in class, but you have all the tools you need to solve it! How could

we turn this into a system of linear equations?