Unit 3: Exponential and Logarithmic Functions Review

Unit 3: Exponential and Logarithmic Functions Review

Review

• Exponential Functions

• Graphs of Exponential Functions

• Compound interest and "e"

• Logarithmic Functions

• Graphs of Logarithmic Functions

• Solving Exponential and Logarithmic Equations

Poll

How are you feeling about the Unit 3 Test?

• Good

• Could use some help

• I'm not sure

Multiple Select

Exponential functions are of the form y = a $\cdot$  $b^x$  . What do a and b represent? (There are 2 correct answers, one correct answer for a and one correct answer for b)

• a represents the initial amount

• a represents the slope

• b represents the linear growth

• b represents the growth / decay rate

Multiple Choice

If the initial population of turtles was 20 and grew to 25 after the first year, which of the following functions best models the populations of turtles, P, with respect to the number of years, t, if the population growth of rats is considered to be exponential?

• P = 20(1.2)^t

• P = 5t + 200

• P = 20(1.25)^t

• P = 5t²

Multiple Choice

For exponential functions of the form y = a $\cdot$  $b^x$  , b represents the exponential growth/decay rate. We know the function is an exponential decay function if

• b = 1

• b > 1

• b > 2

• 0 < b < 1

Multiple Choice

For exponential functions of the form y = a $\cdot\ b^x$ , b represents the exponential growth/decay rate. We know the function is an exponential growth function if b

• b = 1

• b > 1

• b > 2

• 0 < b < 1

Multiple Choice

Is y =  $\frac{1}{2}$   $\cdot$  $\left(\frac{3}{2}\right)^x$ exponential growth or decay?

• Growth

• Decay

Multiple Choice

Is y = 2000 $\cdot$  $\left(\frac{1}{4}\right)^x$ growth or decay? 

• growth

• decay

Multiple Choice

Which equation matches the graph?

• y = 2^x+3

• y = 2^x

• y = 2^x + 3

• y = 2^-x

Multiple Choice

Which equation matches the graph?

• y = 2^x+3

• y = 2^x

• y = 2^x + 3

• y = 2^-x

Compound interest formula review:

• P₀ = initial amount invested

• r = interest rate (as a decimal)

• n = number of compoundings / year

• t = number of years

Multiple Choice

Which is the following is the compound interest formula?

• P(t) = P₀ (r/n)^nt

• P(t) = P₀ (1 + r/n)^nt

Multiple Choice

A new savings account is opened with $1000 and gains 4% every year. What is the exponential function?

• f(x) = 1000(1+4)^x

• f(x)= 1000 (1+0.04)^x

• f(x)= 1000(1-0.04)^x

• f(x)= 1000(0.04)^x

Multiple Choice

What is the logarithmic form function?

• log_y b = x

• log_x b = y

• log_b x = y

• log_b y = x

Open Ended

Change this log function to be in the form of an exponential equation: log_t m = z

Multiple Choice

Evaluate:

ln e⁵ = ?

• 5

• 2.718

• 1

• 10

Open Ended

Evaluate:

log 100 = ?

Open Ended

Evaluate:

log₂ 32 = ?

Multiple Choice

Rewrite log₂ 16 = 4 in exponential form.

• 2¹⁶ = 4

• 4² = 16

• 2⁴ = 16

• 16⁴ = 2

Open Ended

Log rule for addition: log_b x + log_b y = ?

Open Ended

Log rule for subtraction: log_b x - log_b y = ?

Multiple Choice

Log rule for exponents: log_b x^a

• b ⋅ log_a x

• a ⋅ log_b x

• x ⋅ log_b a

Open Ended

Expand this logarithm expression: log₂ 12xy⁵

Open Ended

Condense this logarithm: 3log 3 - log 2

Multiple Choice

What is the correct transformed equation for the graph?

• y = log₄ (x) + 2

• y = log₄ (x) - 2

• y = log₄ (x-2)

• y = log₄ (x+2)

Multiple Choice

What is the range of the function graphed?

• (-2,  $\infty$ )

• (0 ,  $\infty$ )

• (- $\infty$  , -2)

• (- $\infty$  ,  $\infty$ )

Multiple Choice

What is the domain of the function graphed?

• (-2,  $\infty$ )

• (0 ,  $\infty$ )

• (- $\infty$  , -2)

• (- $\infty$  ,  $\infty$ )

Open Ended

What is the vertical asymptote of the function graphed log₄(x+2) ?

Multiple Choice

Solve for x:

log₃ 2 + 2log₃ x = log₃ (7x-3)

• x = 1/2 and x=3

• 1/2

• x = -1/2 and x=3

• -3

Multiple Choice

Solve for x:

2^x + 16 = 24

• 1

• 2

• 3

• 4