Exponential and Logarithms

Presentation

•

Mathematics

•

8th - 12th Grade

•

Hard

Mitchell Stanberry

Used 6+ times

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5 Slides • 32 Questions

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^xdetermine 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

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 ?

-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 Blanks

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

Type answer...

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 Blanks

$\log_636$

Type answer...

Fill in the Blanks

$\log_3\frac{1}{9\ }$

Type answer...

Fill in the Blanks

$\log_{\frac{1}{10}}10,000=x$

Type answer...

Fill in the Blanks

$\log_{\sqrt{3}}\ 9=x$

Type answer...

Fill in the Blanks

$\log_{x\ }\frac{1}{64}=-3$

Type answer...

Multiple Choice

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

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?

Exponential and Logarithms

Solving and Graphing Exponentials

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