Exponential Models

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(1 - 0.30)^x

• y=30(5000)^x

• y=5000(1 + 0.30)^x

• y=5000x^x

Tags

CCSS.HSA.CED.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

The amount of ants in a colony, f, that is decaying can be modeled by

f(x) = 800(.87)^x, where x is the number of days since the decay started.

Suppose f(20) = 49. Which of the following is true?

• After 20 days, there are 49 ants in the colony.

• After 49 days there are 20 ants in the colony.

• The amount of ants times 20 is 49.

• After 20 days the amount of ants remaining decreases by 49.

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

What does the y-intercept of the graph represent?

• The amount of grams the material is gaining.
• The amount of grams the material is losing.
• The amount of grams remaining after so many years.
• The initial amount of grams.

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.SSE.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

The amount of downloads for an album on iTunes, g(d), where d is the number of days since the album was first uploaded can be represented as
g(d) = 5^1.5d
How many downloads will the album have after 3 days?

• 125
• 11
• 1398
• 140

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.LE.A.1

What is the Domain of this exponential function?

• y=1

• x=0

• All Real Numbers

• x>0

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.B.5

CCSS.HSF.LE.A.1

What is the Range of this function?

• y> 0

• x> 0

• All Real Numbers

• y>0

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What is the y-intercept of the function f(x)=2(4)^x ?

• 2

• 4

• (4)^x

• 8

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

What is the horizontal asymptote for the graph of

f(x)=2(3)^x ?

• y=2

• y=0

• y=3

• x=-4

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSF.LE.A.3

Determine the range for the function
f(x)=3(2)^x-4+5

• [5,∞)
• (5,∞)
• [4,∞)
• (4,∞)

Tags

CCSS.HSA.REI.D.10

Determine the asymptote for the function
f(x)=3(2)^x-4+5

• x=4
• y=4
• x=5
• y=5

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSF.LE.A.2