Exponential and Logarithms

Exponential and Logarithms

Solving and Graphing Exponentials

Multiple Choice

What function is present? 

• Absolute Value
• Exponential Decay
• Linear Equation
• Exponential Growth

Multiple Choice

What is the equation that best represents the graph?

• y=2^y
• y=2^x
• y=2^-x
• y=x²

Multiple Choice

Given y=3^x determine the y-intercept 

• (0,1)
• (0,3)
• No Y-intercept
• y=1

Multiple Choice

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

• Exponential Growth

• Exponential Decay

• Linear

• None

Multiple Choice

Evaluate f(6).

• 355.37
• 3.7
• 47.51
• 6

Multiple Choice

Which of the following functions is represented by this graph?

• f(x)=2(1.2)^x
• f(x)=2(0.75)^x
• f(x)=6(0.75)^x
• f(x)= −2(0.75)^x

Multiple Choice

Using the parent function y=3^x what would the graph of y=3^x+1 look like?

• Horizontal shift left one unit!
• Horizontal shift right one unit!
• Vertical shift up one unit!
• Vertical shift down one unit!

Multiple Choice

What is the horizontal asymptote for the graph of 
f(x)=-2(3)^x+4-8 ?

• y=8
• y=-8
• x=-8
• x=-4

Multiple Choice

What is the base in
f(x)=2(6)^x+3-8 ?

• 2
• 6
• -3
• -8

Multiple Choice

Which functions transforms f(x)=e^x so that is shifts left 5 units and up 3 units?

• f(x) = e^(x+5) - 3

• f(x) = e^(x-3) - 5

• f(x) = e^(x+5) + 3

• f(x) = e^(x-5) - 3

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

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

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

Multiple Choice

Joe deposits $500 in an account with 3% interest compounded quarterly for a period of 5 years. What expression would you type into the calculator to calculate the total amount of money Joe will have after the 5 year period?

• 500(1+.03)⁴⁽⁵⁾

• 500(1+.03/4)⁽⁴⁾⁽⁵⁾

• 500(1+3)⁵

• 500e^(.03)(5)

Fill in the Blank

A man borrowed $6000 for 3 years at a rate of 10% per annum. What is the interest at the end of the period?

Multiple Choice

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

• 14327
• 4309
• 839
• 7680

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

Multiple Choice

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

• Growth
• Decay

Multiple Choice

The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation.

• y=1400(1.09)^x
• y=1.09(1400)^x
• y=1400(.91)^x
• y=1.09^x

Multiple Choice

Suppose you deposit $3000 in a savings account that pays interest at an annual rate of 4%. If no other money is added or withdrawn from the account, how much will be in the account after 10 years?

• $3122.18

• $4994.50

• $4440.73

• $86,776.40

Multiple Choice

The number of research papers in Professor Sycamore area of expertise has been increasing by 5% every year. Given that 30,010 research papers were published this year. Assuming the trend continues, which equation projects the amount of research papers published in x years?

• y = 30,010 (.05)^x

• y = 30,010 (1.05)^x

• y = 30,010 (.95)^x

• y = 30,010 (5)^x

Multiple Choice

Due to its weakening steel industry, Canalave Town has been experiencing a population decline of 10% every year. The current population is 74,000 people. Assuming the trend continues, which equation projects the population in x years?

• y = 74,000 (0.10)^x

• y = 74,000 (0.90)^x

• y = 74,000 (1.10)^x

• y = 74,000 (1.90)^x

Multiple Choice

Use the change of base rule to rewrite this problem:

log₃64

• log(64)/log(3)

• log(3)/log(64)

Fill in the Blank

 $\log_636$  

Fill in the Blank

 $\log_3\frac{1}{9\ }$  

Fill in the Blank

 $\log_{\frac{1}{10}}10,000=x$  

Fill in the Blank

 $\log_{\sqrt{3}}\ 9=x$  

Fill in the Blank

 $\log_{x\ }\frac{1}{64}=-3$  

Multiple Choice

Using the change of base rule, what is this logarithm equivalent to?

• A

• B

• C

• D

Multiple Choice

You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. How long until you have 10mg of caffeine? 

• 19 to 20 hours
• 10 to 20 hours
• 15 to 16 hours
• 5 to 6 hours

Multiple Choice

The foundation of your house has about 1,200 termites. The termites grow at a rate of about 2.4% per day. How long until the number of termites doubles?

• 29 to 30 years
• 23 to 24years
• 15 to 16 years
• 19 to 20 years

Multiple Choice

Katy deposited $90 in a savings account earning 5% interest, compounded quarterly. Which of the following equations could represent the amount of money in her account yearly?