Day 2 - Boot Camp - Exponentials and Exponents

​Doodle Notes

Multiple Choice

Which table of values could represent an exponential function?

• A

• B

Multiple Select

Which THREE situations can be modeled by an EXPONENTIAL function?

• Dan earns 2% interest on his savings account.

• Judy eats 5 boogers each day.

• The deer population increases by 13% each year.

• Jon's car value decreases by 2.5% every 6 months.

Multiple Choice

What is the percent of decrease each year?

• decreases by $10,000 each year

• decreases by $800 each year

• decreases by 80% each year

• decreases by 20% each year

Multiple Choice

A BMW is valued at 50,000.  It depreciates exponentially each year and the car’s value is represented by the function $$b\left(x\right)=50,000\left(0.80\right)^x$$

●

Which statement represents (0.80)?

• The BMW depreciates by 80%.

• The BMW appreciates by 80%.

• The BMW depreciates by 20%.

• The BMW appreciates by 20%.

Multiple Choice

A Samoyed dog is worth $14,000 when it is born.  The value of the dog depreciates each year.  At one year old, $5,600.  At two years old, $2,240.  At three years, $896.

      Choose the TRUE statement.

• The dog depreciates by 80% annually.

• The dog depreciates by a factor of 0.40%.

• The dog depreciates by $8,400.

• The dog depreciates by 60% annually.

Multiple Choice

What is the percent increase?

• 5%

• 10%

• 50%

• 90%

Multiple Choice

Sam has 3,250 followers on social media. His number of followers is decreasing at a rate of 3% per week. Which function represents his number of followers after w weeks?

• $$f\left(w\right)=3,250\left(0.97\right)^w$$

• $$f\left(w\right)=3,250\left(1.03\right)^w$$

• $$f\left(w\right)=3,250\left(1.03\right)^{w-1}$$

• $$f\left(w\right)=3,250\left(0.97\right)^{w-1}$$

Multiple Choice

Bethany is training for a wrestling match. Coach G has her walking 3 miles the first week. She increases the distance by 12% each week.

Which function models how far she will run in any given week?

• $$t\left(n\right)=1.12\left(3\right)^n$$

• $$t\left(n\right)=3\left(1.12\right)^n$$

• $$t\left(n\right)=1.12\left(3\right)^{n-1}$$

• $$t\left(n\right)=3\left(1.12\right)^{n-1}$$

Multiple Choice

The table shows the value of Henry's car for each of the first 3 years after it is purchased.

What will be the approximate value of the car in the 10th year?

• $2,150

• $2,680

• $5,240

• $6,550

Multiple Choice

The Zombie population doubles every day. Beginning with 25, the population can be represented by the function $$f\left(t\right)=25\left(2\right)^t$$ , where t is the number of days.

Which of these is the appropriate domain?

• All real numbers

• All integers greater than or equal to 0.

• All real numbers greater than 25.

• All integers greater than or equal to 25.

Math Response

The student council estimated that they would have 250 people attend the homecoming dance. The number of people who attended was 315. What is the percent of error to the nearest hundredth percent? Type the answer in the blank up to the hundredth place value.

Type answer here

Correct Answer: 20.63

Deg^°

Rad

Multiple Select

Which expressions are equivalent to $$4^{k^2}$$ ? Hint: Choose any number for k and plug it in to check the solution.

• $$4^{4k}$$

• 
  $$16^{\frac{k^2}{2}}$$

• $$16^{2k^2}$$

• $$64^{3k^2}$$

• E $$64^{\frac{k^2}{3}}$$

Multiple Choice

A car is purchased for $30,000. The value of the car depreciates annually so that it is $24,000 after 1 year, $19,200 after 2 years, and $15,360 after 3 years.

Why can this situation be modeled using an exponential function?

• The value of the car depreciates annually by 20%.

• The value of the car depreciates annually by 80%.

• The value of the car depreciates annually by $6,000.

• The value of the car depreciates annually by $4,800.

Multiple Choice

Iodine is a radioactive material with a half-life of eight days. A scientist starts with 100 grams of Iodine-131. Which function can be used to estimate the number of grams of Iodine-131 that remain at the end of x days?

• 
  $$f\left(x\right)=100\left(0.92\right)^x$$

• $$f\left(x\right)=0.92^x$$

• $$f\left(x\right)=100\left(0.5\right)^{\frac{x}{8}}$$

• $$f\left(x\right)=\left(0.5\right)^{\frac{x}{8}}$$

Multiple Choice

James threw a ball from the roof of a building. The ball fell 3 feet in the first second, 9 feet in the next second, and 27 feet in the third second.

Which expression represents the distance the ball fell at the $$n^{th}$$ second?

• $$3^n$$

• $$3n$$

• $$n^3$$

• $$6n-3$$

Multiple Choice

An athlete is training to run a marathon. She plans to run 2 miles in the first week. She increases the distance by 8% each week. Which function models how far she will run in the $$n^{th}$$ week?

• $$t\left(n\right)=1.08\left(2\right)^n$$

• $$t\left(n\right)=2\left(1.08\right)^{n\ }$$

• $$t\left(n\right)=1.08\left(2\right)^{n-1}$$

• $$t\left(n\right)=2\left(1.08\right)^{n-1}$$

Multiple Choice

Which graph matches the equation: $$y=4-x$$

• A

• B

• C

Multiple Choice

Which graph matches the equation: $$y=4\left(0.2\right)^x$$

• A

• B

• C

Multiple Choice

Which graph matches the equation: $$y=4\left(1.2\right)^x$$

• A

• B

• C

​Doodle Notes

Multiple Choice

Simplify.

$$y^5\cdot y^3$$

• $$y^2$$

• $$y^8$$

• $$y^{15}$$

• $$2y^8$$

Multiple Choice

Simplify.

$$-\frac{12x^4y^{-3}z}{20x^8y^{-5}z^{-2}}$$

• $$-\frac{3}{5x^4y^2z^3}$$

• $$-\frac{3}{x^4y^8z}$$

• $$-\frac{3y^2z^3}{5x^4}$$

• $$-\frac{3y^8z}{5x^4}$$

Multiple Choice

Simplify:

$$\left(m^4\right)^2$$

• $$6m$$

• $$m^8$$

• $$m^6$$

• $$2m^4$$

Multiple Choice

Evaluate: $$16^{\frac{3}{4}}$$

• 2

• 4

• 8

• 32

Multiple Choice

Evaluate: $$729^{\frac{2}{3}}$$

• 27

• 9

• 486

• 81

Multiple Choice

Solve: $$3^{x+2}=81$$

• 0

• 1

• 2

• 3

Multiple Choice

Solve: $$216=6^{x+1}$$

• 2

• 1

• 4

• 32

Multiple Choice

The graph and table for $$y=\left(\frac{1}{4}\right)^x$$

• D: $$x>0$$

  R: $$y>0$$

• D: $$y>0$$

  R: All Real Numbers

• D: All Real Numbers

  R: All Real Numbers

• D: All Real Numbers

  R: $$y>0$$

Multiple Choice

Samuel won a contest where he wins a yearly prize for his lifetime. Samuel can choose to be paid $5,000 per year (option 1 in the table) or his payments can be tripled each year, with the first year the payment starting at $100. (Assume Samuel is 15 and will live to be 100 years old).

Which prize option should Samuel choose to earn the most money over his lifetime?

• Option 1 because the total payment is increasing exponentially.

• Option 1 because the total payment is increasing linearly.

• Option 2 because the total payment is increasing exponentially.

• Option 2 because the total payment is increasing linearly.

Multiple Choice

In the graph, s(x) is a linear function and r(x) is an exponential function. Which statement best explains the behavior of the graphs of the functions as x increases?

• $$r\left(x\right)$$ eventually exceeds $$s\left(x\right)$$ because the rate of change of $$s\left(x\right)$$ increases, where as the rate of change of $$r\left(x\right)$$ is constant.

• 
  $$r\left(x\right)$$ eventually exceeds $$s\left(x\right)$$ because the rate of change of $$r\left(x\right)$$ increases as x increases, where as the rate of change of $$s\left(x\right)$$ is constant.

• $$s\left(x\right)$$ eventually exceeds $$r\left(x\right)$$ because the rate of change of $$r\left(x\right)$$ increases, where as the rate of change of $$s\left(x\right)$$ is constant.

• 
  $$s\left(x\right)$$ eventually exceeds $$r\left(x\right)$$ because the rate of change of $$s\left(x\right)$$ increases, where as the rate of change of $$r\left(x\right)$$ is constant.

Multiple Choice

Which equation represents exponential decay?

• $$y=0.5x^3$$

• $$y=0.5\left(1.07\right)^x$$

• $$y=0.5x^2-x$$

• $$y=0.5\left(0.87\right)^x$$

Multiple Choice

Which equation represent exponential growth?

• $$y=2x^3$$

• $$y=\frac{1}{3}x^2-x$$

• $$y=2000\left(0.82\right)^x$$

• 
  $$y=2000\left(1.82\right)^x$$

Multiple Choice

Which equation correponds to the graph given?

• $$y=2^x+2$$

• 
  $$y=2^x-2$$

• $$y=\left(\frac{1}{2}\right)^x-2$$

• $$y=\left(\frac{1}{2}\right)^x+2$$

Multiple Choice

Which equation corresponds to the graph given?

• 
  $$y=3\left(2\right)^x$$

• $$y=2\left(3\right)^x$$

• $$y=3\left(2\right)^x-1$$

• $$3\left(2\right)^x+1$$

Multiple Choice

If $$y=10\left(2.5\right)^t$$ represents the number of bacteria in a culture at time t, how many will there be at time $$t=6$$ .

• 2,441

• 244

• 24

• none

Multiple Choice

A $60,000 piece of machinery's value depreciates at a rate of 11% per year. About what will its value be in 5 years?

• $47,526

• $42,298

• $33,504

• $37,645

Dropdown

Which option gives the greater ending balance?​

Select answer

Option 1: Put $100 in an account that pays 5% interest compounded annually for 5 years at Regent Bank.



Option 2: Keep $105 in your room under your mattress and add $4 to it each year for 5 years.

Dropdown

State if the example is exponential growth or decay. $$y=46\left(1.86\right)^x$$ ​

Select answer

Dropdown

State if the example is exponential growth or decay.​



​ $$y=2\left(0.17\right)^x$$



​

Select answer

Dropdown

State if the example is exponential growth or decay.​ $$y=10\left(1.35\right)^x$$



​

Select answer

Labelling

Identify each item using the equation given.

Drag labels to their correct position on the image

196

1.16

0.16

Labelling

Identify each item using the equation given.

Drag labels to their correct position on the image

0.38

12

0.62

Multiple Choice

If a $5,000 piece of equipment loses value at a rate of 0.5% per year, which equation represents the value after 5 years?

• 
  $$y=5000\left(5\right)^5$$

• 
  $$y=5000\left(0.995\right)^5$$

• $$y=5000\left(1.05\right)^5$$

• $$y=5000\left(0.95\right)^5$$

Labelling

Identify each item using the equation given.

Drag labels to their correct position on the image

0.57

210

0.43

Multiple Choice

Each year, new computers are built with better technology, making older ones less valuable. If the computer loses value at a rate of 2.5% per year, how much will a $1,500 computer be worth in 10 years?

• $1,165

• $1,920

• $84.47

• $13,970