Algebra 2 - Lesson 6.1 - 6.3 Review

Algebra 2

Lesson 6.1 - 6.3 Review

6.1 - 6.3 Concepts

• Graph Exponential Functions

• Solve Exponential Growth and Decay Problems

• Solve problems involving compound interest

• Solve problems involving compounding continuously

• Convert between Exponential and Logarithmic

• Evaluate Log and Ln functions

• Solve Exponential and Logarithmic Equations

Multiple Choice

What type of function is y = 7(5/4)^x?

• Exponential Growth
• Exponential Decay
• Linear
• None of the above

Multiple Choice

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

• $1,225,54
• $2,225.54
• $22,255.40
• $225.54

Multiple Choice

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

• Growth
• Decay

Multiple Choice

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years?

• $15,415.94

• $15,683.28

• $15,927.56

• $16,349.72

Fill in the Blanks

Solve for x. Round to 4 decimal places, if necessary.

ln (3x - 2) = 3

Multiple Choice

Mark took a loan out for $25,690 to purchase a truck. At an interest rate of 5.2% compounded monthly, how much total will he have paid after 5 years?

• $33,299.42

• $33,672.68

• $34,157.04

• $34,710.88

Multiple Choice

Is the pictured graph growth, decay, or linear or none?

• Exponential Growth

• Exponential Decay

• Linear

• None

Multiple Choice

Write the following logarithm as an exponential:
 $\ln\left(5\right)=x$  

•  $5^x$  

•  $e^x=5$  

•  $e^5=x$  

•  $x^5=2.71$  

Multiple Choice

Rewrite the logarithm in exponential form:
 $\log_x25=3$  

•  $x^3=25$  

•  $3^x=25$  

•  $25^3=x$  

•  $25^x=3$  

Fill in the Blanks

 $\log_749=$  

Multiple Choice

Rewrite the logarithm in exponential form:
 $\log_yx=10$  

•  $y^{10}=x$  

•  $x^{10}=y$  

•  $10^y=x$  

•  $y^x=10$  

Multiple Choice

 $\log_3243=$  

Evaluate

• 4

• 5

• 6

• 7

Multiple Choice

Emily’s parents put $1,500 in her bank account for college tuition. At an interest rate of 8.25% compounded semiannually,what will be the balance after 18 years?

• $6,273.50

• $6,314.08

• $6,385.72

• $6,427.94

Multiple Choice

 $\log_{ }1000$  

Evaluate

• 3

• 0

• 1

• 4

Multiple Choice

Write an equation that models the following situation:

Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

• y=6(0.14)^x

• y=6(1+14)^x

• y=6(1.14)^x

• y=6(0.86)^x

Fill in the Blanks

Solve the equation for x. Round to 4 decimal places, if necessary.

Multiple Choice

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81
• log₈₁3 = 4
• log₃81 = 4
• log₄81 = 3

Multiple Choice

Caiden earned $475 from mowing lawns last summer.He deposited this money in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 years?

• $827.52

• $831.10

• $839.45

• $846.80

Fill in the Blanks

Solve for x. Round to 4 decimal places, if necessary.

log (2x+6) = 2

Multiple Choice

Is y = 5(1.04)^x growth or decay?

• Growth

• Decay

Multiple Choice

What is the balance of $6000 compounded annually at a rate of 4% for 10 years?

• $8,881.47
• $7,432.93
• $8,400
• $6,500

Multiple Choice

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

• $23,219.72
• $136.72
• $51,710.94
• $16,710.94

Fill in the Blanks

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months? (Round your answer to the nearest mosquito.)

Multiple Choice

Is y = 4(.20)^x growth or decay?

• Growth
• Decay

Multiple Choice

What is the decay rate in the following model?

A=1200(.85)⁶

• 1200

• .15

• .85

• 6

Multiple Choice

What type of function is f(x)=2(1/7)^x ?

• Exponential Growth

• Linear

• Exponential Decay

• None of the Abovee

Multiple Choice

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

• y = 15(35)^x
• y = 15(1.35)^x
• y = 15(0.35)^x
• y = 35(1.15)^x

Fill in the Blanks

 $\log\ \left(3x+1\right)=0$  

Solve for x.  Round to 4 decimal places, if nessary.

Multiple Choice

Is this exponential growth or decay?

• Growth

• Decay

• Linear

Multiple Choice

 $\log_232=$  

Evaluate

• 2

• 3

• 4

• 5

Multiple Choice

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(0.7)^x
• y=30(5000)^x
• y=5000(1.3)^x
• y=5000x^x

Fill in the Blanks

Solve for x. Round to 4 decimal places, if necessary.

ln x = -3

Multiple Choice

The common logarithm has what base?

• 10

• 0

• e

• -e

Multiple Choice

Write an equation that models the following situation:

Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

• y=6(0.14)^x

• y=6(1+14)^x

• y=6(1.14)^x

• y=6(0.86)^x

Fill in the Blanks

Willie invests $8,515 in a retirement account with a fixed annual interest rate of 5% compounded continuously. What will the account balance be after 20 years?

Open Ended

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