Topic 5 Exponents and Exponential Functions

Which of the following is true about the function: f(x) = .5(2)^x?

• The function shows exponential growth.

• The function shows exponential decay.

• The function is a linear function.

• The y intercept is 2.

What is the explicit rule for the sequence:
11, 22, 44, 88...

• a_n = 2(11)^n-1
• a_n = 11x2
• a_n = 11(2)^n-1

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

What is the recursive equation that describes the sequence:

3, 15, 75...

• A_n = 12 ∙ A_n-1

• A_n = 1/5 ∙ A_n-1

• A_n = 5∙ A_n-1

• A_n = 3 ∙ A_n-1

Which ordered pair is a solution to the function y = -8(½)^x

• (–2, –30)

• (0, 0)

• (1, –3)

• (3, –1)

f(x) = 2(3)^x

g(x) = 3x + 4

Which statement is true about the two functions when x = 3 ?

• The value of f(x) exceeds the value of g(x) by about 50.

• The value of g(x) exceeds the value of f(x) by about 50.

• The value of f(x) exceeds the value of g(x) by about 41.

• The value of g(x) exceeds the value of f(x) by about 41.

The attendance at the art museum at the New Year’s opening was 250 people. The attendance has been increasing at a rate of 3% each month. How many people will attend by the end of a year?

• 356
• 265
• 5825
• 1329

Given the following table, which has a greater rate of change over the interval [-1, 1]?

• f(x)
• g(x)
• Neither 
• Same 

Find x when f(x) = 3^x and g(x) = 4, what is f(x) + g(x).

• 3^x + 4

• 4(3)^x

• 7^x

• 3^x - 4

Is the table linear, exponential or neither?

• Linear
• Exponential
• Neither