Topic 6 Review (Analytical Algebra 2)

Topic 6 Review (Analytical Algebra 2)

By Edward Jones

​Some thoughts...

• The following questions will be a somewhat thorough simulation of the upcoming test!

• If you find that there are questions you're not doing well on, feel free to give those areas extra study time!​

​Sections

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• 6.1 Key Features of Exponentials

• 6.2 Compound Interest/Exponential Models​

• 6.3 Intro to Logarithms

• 6.4 Logarithm Functions/Graphs

• 6.5 Properties of Logarithms

• 6.6 Exponential/Logarithmic Equations​

Multiple Choice

One of these functions is exponential decay. Which one?

• $$f\left(x\right)=4\left(\frac{2}{3}\right)^x$$  

• $$f\left(x\right)=2^x$$  

• $$f\left(x\right)=\frac{1}{2}\left(3\right)^x$$  

• $$f\left(x\right)=x^2-4$$  

Multiple Choice

A particular population of endangered fish is dropping at a rate of 4% per year. You determine the current population to be 3,000 left. Which function models this situation?

• $$F\left(t\right)=3000\left(.04\right)^t$$  

• $$F\left(t\right)=3000\left(.96\right)^t$$  

• $$F\left(t\right)=3000\left(1.04\right)^t$$  

Multiple Choice

Using the previous problem's model, how many fish would there be 10 years from now?

$$F\left(t\right)=3000\left(.96\right)^t$$  

• Around 500

• Around 1000

• Around 2000

• Around 2500

Multiple Choice

$1000 was deposited into a savings account that earned interest at a rate of 3% compounded semi-annually for 20 years. About how much money is in the account by then?

• $991.57

• $1299.12

• $1563.08

• $1825.98

Multiple Choice

All of the following are equal to 3 except one option. Which one?

• $$\log_28$$  

• $$\log_327$$  

• $$\log_464$$  

• $$\log_5150$$  

Multiple Choice

Find $$\ln\left(-3\right)$$  .

• About -.9275

• About 2.238

• Undefined

Multiple Choice

Solve for x.

$$\log_4\left(5x+1\right)=4$$  

• x = 51

• x = -25

• x = 8

• No solution

Multiple Choice

Determine which functions matches the following graph:

• $$f\left(x\right)=\log_2\left(x+1\right)-3$$  

• $$f\left(x\right)=\log_2\left(x-1\right)+3$$  

• $$f\left(x\right)=\log_2x$$  

Fill in the Blanks

Use a calculator and the change of base formula to find:

$\log_{21}91$  

Round to 2 decimal places.

Multiple Choice

Solve $$4^x=21$$ . Round to 3 decimal places. 

• $$x\approx1.75$$  

• $$x\approx2.196$$  

• $$x\approx-3.17$$  

• $$x\approx0.197$$  

Multiple Choice

What is $$\log_7\left(\frac{3x^7}{y^2}\right)$$ equivalent to when fully expanded? 

• $$\log_7\left(3x\right)-2\log_7\left(y^2\right)$$  

• $$\log_73+\log_7\left(x^7\right)-\log_7\left(y^2\right)$$  

• $$\log_73+7\log_7\ x-2\log_7\ y$$  

Multiple Choice

Solve $$2^{\left(4x+7\right)}=8^{\left(x-4\right)}$$  .

• x = 3/2

• x = -19

• x = 28

• x = -5

• Use this review game as a study guide

• If questions didn't go well, revisit them before the test!​

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​That's it!

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