EOC Review: Exponentials

Evaluate the power. NO DECIMALS. Leave answers as
simplified improper fractions when necessary.

Evaluate the power. NO DECIMALS. Leave answers as
simplified improper fractions when necessary.

Evaluate the expression. NO DECIMALS. Leave answers as
simplified improper fractions when necessary.

Evaluate the expression. NO DECIMALS. Leave answers as
simplified improper fractions when necessary.

Simplify each expression. Do not leave negative exponents
in your answer.

Simplify each expression. Do not leave negative exponents
in your answer.

Solve each equation.

Solve each equation.

Solve each exponential inequality. Write each answer in
INTERVAL NOTATION

Solve each exponential inequality. Write each answer in
INTERVAL NOTATION

Identify each of the following functions as
exponential growth or decay. Then, give the rate of
growth or decay as a percent.

Identify each of the following functions as
exponential growth or decay. Then, give the rate of
growth or decay as a percent.

Growth

Decay

r = 7% inc

r = 12% dec

Write an exponential growth function to model each situation. Then
find the value of the function after the given amount of time.

22. The value of a house is $275,000 and is appreciating in value at a
rate of 7% each year. Find the value of the house in 5 years. (Round to
2 decimal places)

a. Write an exponential growth function, in terms of t, that represents
the above situation.

b. Find the value of the house after 5 years.

Write an exponential growth function to model each situation. Then
find the value of the function after the given amount of time.

22. The value of a house is $275,000 and is appreciating in value at a
rate of 7% each year. Find the value of the house in 5 years. (Round to
2 decimal places)

a. Write an exponential growth function, in terms of t, that represents
the above situation.

b. Find the value of the house after 5 years.

Stretch by 3

Reflect over x-axis

Stretch by 2

Shift right 5

Shift left 3

Shift down 4

Stretch by 2

Shift right 1

Shift down 2

16 Teams

Multiple Choice

Use the function, M=.05(2)^t, where M is the amount of money you have after t days.
Will the function be INCREASING or DECREASING?

• Increasing
• Decreasing

Multiple Choice

Use the function, M=.05(2)^t, where M is the amount of money you have after t days.
How much money will you have after 14 days?

• $ 819.20
• $ 8,192.00
• $ 1.40
• $ 819.02

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

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

• y=8(15,000)^x
• y=15,000(1.08)^x
• y=15,000(0.92)^x
• y=15,000(0.08)^x

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

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

Some banks charge a fee for a savings account that is left inactive for an extended period of time. The equation y = 5000(0.98)^x represents the amount remaining, y, of one account that was left inactive for a period of x years. What does the number 5000 represent in this situation?

• A fee charged for an inactive account
• The percent of money in the account after x years
• The amount of money in the account initially
• The amount of money in the account after x years

Multiple Choice

For the function f(x) =6(3)^x , what is the y-intercept?

• (6,0)
• (3,0)
• (0,3)
• (0, 6)

Multiple Choice

What is a, the starting term, for the function: f(x) = 300(1.16)^x?

• 300
• 1.16
• .16
• x

Multiple Choice

What is the asymptote?

• x=0
• y=0
• x=1
• y=1

Multiple Choice

Classify the following graph.

• Exponential Growth

• Exponential Decay

• Linear

• Quadratic

Multiple Choice

Classify the following graph.

• Exponential Growth

• Exponential Decay

• Linear

• Quadratic

Multiple Choice

Find the common ratio: 4, -16, 64, -256, ...

• r = -4

• r = 2

• r = -2

• r = 4

Multiple Choice

Write the explicit formula for the geometric sequence.

• a_n = 4(3)^n-1
• a_n = 3(4)^n-1
• a_n = -4(3)^n-1
• a_n = 3(-4)^n-1

Multiple Choice

Where would the asymptote be for this graph?

• y = 4
• y = -4
• x = 3
• x = -3

Multiple Choice

Does the following represent growth or decay?

y=1/2(3)^x+2

• Growth

• Decay

Multiple Choice

What is the y-intercept of the function?

• 2

• 3

• 1

• -2

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 Select

What is the domain of

$$f\left(x\right)=5^x$$  

Choose 2.

• All real numbers

• (-∞,∞)

• All real numbers greater than 1

• All real numbers less than 0

Multiple Select

What is the domain of

$$f\left(x\right)=\left(2\right)5^x$$  

• All real numbers

• (-∞,∞)

• All real numbers greater than 1

• All real numbers less than 0

Multiple Select

What is the range of

$$f\left(x\right)=\left(2\right)5^x$$  

• y>0

• (0,∞)

• All real numbers greater than 1

• All real numbers less than 0

Multiple Choice

For the function f(x) = -3^x + 3 find f(0).

• 0

• -3

• 2

• -1

Multiple Choice

Evaluate f(-2) if f(x) = 2^x+ 3.

• -1

• 1

• 13/4

• -7

Multiple Choice

What type of function is f(x)=2(1/7)^x ?

• Exponential Growth

• Linear

• Exponential Decay

• None of the Above

Multiple Choice

Is the table linear, exponential, or neither?

• Linear

• Exponential

• Nether

Multiple Choice

Which table represents the following equation?

f(x)=2(3)^x

Multiple Choice

The range of

$$y=3^x$$  is 1,3,9,27.... What is the domain of the function?

• (-∞,∞)

• (0,∞)

• {1,2,3,4,...}

• {0,1,2,3,....}

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

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

• Horizontal Shift to the right 1 unit

• Horizontal shift to the left one unit

• Vertical shift one unit up

• Vertical shift one unit down

Multiple Choice

The function y = 125(1.13)^x represents Mr. Gantz's recent investments where x is measured in years.  Which is NOT true?

• Mr. Gantz initial invested $125
• Mr. Gantz's money grows by 13% per year
• After 4 years Mr. Gantz will have about $203.81
• Mr. Gantz earns more money in year one than in year 5

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

Identify the initial value:

y = 6.87 (4)^x

• a = 4

• a = 6.87

• a = 3

• a = 1

Multiple Choice

The next term of the geometric sequence

4, 16, 64, ...

is

• 256

• 132

• 120

• 150

Multiple Choice

What is the domain and range of the function y=2^x ?

Use the graph to help!

• Domain: (- ∞, + ∞)

  Range: (0, + ∞)

• Domain: (- ∞, + ∞)

  Range: (1, + ∞)

• Domain: (- 2, + ∞)

  Range: (0, + ∞)

• Domain: (- ∞, + ∞)

  Range: ( - ∞, + 0)

Multiple Choice

Compare f(x) = 3^x- 4 with the basic function g(x) = 3^x

• 4 units up
• 4 units to the left
• 4 units to the right
• 4 units down

Multiple Choice

What kind of transformation is represented?

• up 1 unit
• left 1 unit
• right 1 unit 
• down 1 unit

Multiple Choice

Which function represents the table of values? 

• f(x) = 4x
• f(x) = x³
• f(x) = 4^x
• f(x) = 4^x-1

Multiple Choice

What is the recursive rule for the sequence:

-2, 12, -72, 432, ...

• a_n = -2(-6)^n-1

• a_n =a_n-1 + 10

• a_n = -6 (a_n-1)

• a_n = a_(n-1) - 6

Multiple Choice

What is the end behavior of the graph?

• x → -∞, y →+∞

  x → +∞, y →-∞

• x → - ∞, y → 3

  x → + ∞, y → + ∞

• x → -∞, y → + ∞

  x → + ∞, y → - ∞

• (-∞, +∞)

Multiple Choice

What is the x intercept of the graph?

• (0, 5)

• (0, 4)

• (0, 4)

• there are no x intercepts

Multiple Choice

Is the function shown increasing or decreasing?

• increasing

• decreasing

• trick question

• not enough information

Multiple Choice

For the function $$f\left(x\right)=-5^x-3$$  , what is the domain and range?

• Domain: $$\left(-\infty,\ \infty\right)$$  

  Range: y < -3

• Domain: $$\left(-\infty,\ \infty\right)$$  

  Range: y > -3

• Domain: $$\left(-\infty,\ \infty\right)$$  

  Range: $$\left(-\infty,\ \infty\right)$$  

• Domain: y < -3

  Range: $$\left(-\infty,\ \infty\right)$$  

Multiple Choice

For the function $$f\left(x\right)=-5^x-3$$  , find the rate of the change over the interval [0,1]

*remember: $$\frac{y_2-y_1}{x_2-x_1}$$  

• -4

• 4

• 1

• 0

Multiple Choice

For the function $$f\left(x\right)=-5^x-3$$  , as x is approaching $$-\infty$$  , what is y doing?

• y is approaching -3

• y is approaching 3

• y is approaching $$\infty$$  (increasing)

• y is approaching $$-\infty$$  , decreasing

Multiple Choice

For the function $$f\left(x\right)=-5^x-3$$  , as x is approaching $$\infty$$  , what is y doing?

• y is approaching -3

• y is approaching 3

• y is approaching $$\infty$$  (increasing)

• y is approaching $$-\infty$$  , decreasing

Multiple Choice

For the function $$f\left(x\right)=-5^x-3$$  , is it increasing or decreasing?

*(HINT: read the graph from left to right)*

• increasing

• decreasing