Math 112-008 Exam 4

Evaluating Exponentials

100

Evaluate y=6^x-3 at x=4.6, 2.3, and 8.2

17.6, 0.29, 11127.2

200

If k(x)=3^x+2, find the y intercept

k(0)=3

(0,3)

300

Write the compound interest formula if the amount is compounded MONTHLY

A=(1 + r/12)^12t

400

$2,500 at 7.75% is compounded quarterly for 10 years. What is the amount after these 10 years? 

A= 2500(1 + 0.0775/4)⁴⁽¹⁰⁾

A=$5,386.4

500

Solve

(√3)^2x-1=27

x= 7/2 or 3.5

rewrite square root and change of base

Laws of log (Expanding/Condensing)

100

Expand log₂(7x)

log₂(7) + log₂(x)

200

Evaluate the following

log₂(1/8)

log_x125=3

log₂(64) + log₂(2)

set everything = to x: circle method 

x=-3

x=5

x=7

300

Condense 1/2ln(x²) + ln(y) - log_e(z)

ln[ (x^2/3y)/(z²)]

400

Expand ln[(x²y)/square root(z)]

2ln(x) + ln(y) - 1/2ln(z)

500

Expand log₂√(6x⁷)/z³ 

1/2log₂6 + 7/2log₂x - 3/2log₂z

Solving Exponential/Log Equations

100

Solve

ln(2x-1)=ln(x+4)

x=5

200

Solve 4^x+1=32

change of base

x= 3/2

300

e^2x -7e^x + 10=0

ln(5), ln(2)

400

log₃(x²- 4x -12)=2

x=7, -3

500

Solve log(x) + log(6-x)=log(8)

x=2,4

Systems of Equations

100

3x -3y + z=0

y + 3z=8

z=3

(x,y,z)= (-2,-1,3)

200

Find the complete solution of the linear system, or show that the system is inconsistent

x + y + z = 8

x + 3y + 3z = 182

x + y − z = 5

(x,y,z)=(3,2,3)

300

Solve this system. List smaller y value then the larger

x+y²=0

5x+7y²=18

-3, 3

400

7x+y+5z=27

4x+3y+5z=21

6x+y+2z=9

x=0

y=-3

z=6

500

x+y+z=6

3x+3y+3z=18

2x+2y+2z=12

All real numbers

REMEMBER THESE

100

Which is the red graph and blue graph? what are the asymptotes/ intercepts?

blue- y=e^x or y=a^x, HA at y=0, (0,1)

red- y=log(x) or y=ln(x), HA at x=0, (1,0)

200

How can we rewrite the following:

square root(x)

1/x

x^1/2, x^-1

300

Change of base formula; when to use it

Log_x(y)= [log(y)]/[log(x)] 

Use it when asked to evaluate log for decimal; question usually states to use this equation and round

400

ln= ?

What is the implied base (little number) for log when there is no number there?

log_e

10 (log₁₀)

500

What does a reflection over the x and y axis look like in a function (which variable changes and how)

how do you know if a graph is going to shift up, down, left, or right

reflection over x axis--> y is negative. example: f(x)= -2^x

reflection over y axis--> x is negative. example: f(x)= 2^-x

up: add to function. down: subtract from function--> f(x)= 2^x +/- 1

right: subtract from x. left: add to x--> f(x)= 2^{x +/- 1}