Unit 4, Quiz 2 Review

Unit 4, Quiz 2 Review

Exponential Growth and Decay

​We can model exponential growth and decay with percentages using the formulas on the right.
a represents the initial value
r is the rate (%) written as a decimal
t is the time

Watch the video on the right if you need an example on how to apply these formulas or look at your Guided Notes #4

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Exponential Growth and Decay

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.

• $$y=6(0.14)^x$$

• $$y=6(14)^x$$

• $$y=6(1.14)^x$$

• $$y=6(0.86)^x$$

Multiple Choice

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

• $$y=5000(0.7)^x$$

• $$y=30(5000)^x$$

• $$y=5000(1.3)^x$$

• $$y=5000^x$$

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

Multiple Choice

A collectible car has been going up in price by 10% each year. If the car is already worth $29,000, how much will the car be worth in 5 years?

• $0.29
• $2,900,000,000
• $46,704.79
• $145,000

• Compound Interest causes interest and account balances to grow.
  To calculate the balance in an account we can use the formula on the right.

• For interest compounded
  annually n =1
  semiannually n =2
  quarterly n = 4
  monthly n = 12
  daily n = 365
  
  

​Compound Interest Formula

Watch the video on the right if you need an example on how to apply these formulas or look at your Guided Notes #5

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Compound Interest

Multiple Choice

Find the balance in the account after the given period.

$3400 principal earning 3.6% compounded annually after 2 years

• $3,420.43

• $3,649.21

• $3,675.39

• $6,288.64

Multiple Choice

Find the balance in the account after the given period.

$5000 deposit earning 1.5% compounded quarterly after 3 years

• $5,229.70

• $7,604.38

• $7,777.27

• $5,538.86

Multiple Choice

Find the balance in the account after the given period.

$13,500 deposit earning 3.3% compounded monthly after 1 year

• $13,611.38

• $14,898.84

• $13,537.13

• $13, 952.30

A logarithm is the inverse of an exponential function.

We can write exponential functions as logarithms using the rule on the right.

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​Logarithms

Watch the video on the right if you need an example on how to re write exponential functions as logarithms or look at your Guided Notes #6

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Logarithms

Multiple Choice

Write in exponential form

$$\log_232=5$$

• $$2^{-5}=32$$

• $$2^{32}=5$$

• $$2^5=32$$

• $$32^5=2$$

Multiple Choice

Write in exponential form. $$\log_2\left(\frac{1}{8}\right)=-3$$

• $$2^{-3}=\frac{1}{8}$$

• $$2^{\frac{1}{8}}=-3$$

• $$-3^2=\frac{1}{8}$$

• $$-3^{\frac{1}{8}}=2$$

Multiple Choice

Rewrite $$3^4=81$$ in logarithmic form.

• $$\log_34=81$$

• $$\log_{81}3=4$$

• $$\log_381=4$$

• $$\log_481=3$$

Multiple Choice

 Convert to logarithmic form: $$2^9=512$$  

• $$\log_9512=2$$  

• $$\log_2512=9$$  

• $$\log_29=512$$  

• $$\log_92=512$$  

Since exponential and logarithmic functions are inverses of each other. We can solve exponential equations by rewriting them as a logarithm.

Solving Exponential Equations
1. Get the exponent term by itself.
2. Re write in logarithmic form.
3. Solve for x.

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Solving Exponential Equations

Multiple Choice

Solve: $$10^{3x}-1=5$$   Round your answer to the nearest thousandth (3 decimal places).

• $$0.259$$

• $$0.778$$

• $$3.778$$

• $$0.954$$

Since exponential and logarithmic functions are inverses of each other. We can solve logarithmic equations by rewriting them as an exponential equation.

Solving Logarithmic Equations
1. Get the logarithmic term by itself.
2. Re write in exponential form.
3. Solve for x.

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Solving Logarithmic Equations

Multiple Choice

$$\log_8\left(4x+4\right)=2$$

• $$x=15$$

• $$x=12$$

• $$x=10$$

• $$x=3$$