Comparing Exponential Equations

An exponential function is defined by \(f\left(x\right)=a\left(b\right)^x\) .
What does the variable a represent? Select all options that are true.

• The starting value of the function.

• The growth rate

• the decay rate

• The y value when x = 0

• The x value when y = 0.

Tags

CCSS.HSF.LE.B.5

Which function has a greater rate of change over the interval [-2, 0]?

• Function A

• Function B

• Both functions have the same rate of change over the interval.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Which function has a greater y-intercept?

• Function A

• Function B

• Both functions have the same y-intercept

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Which function has a greater y-intercept?

• Function A

• Function B

• Both functions have the same y-intercept.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Compare the following functions: Y(x) is shown in the table and f(x) = 95(1.25)^x Which statements are true? Show work (hint: make a table for f(x) and find the growth factor for y(x)).

• When x>3, f(x) will exceed y(x)

• g(x) will reach 120 first.

• f(x) has a smaller y intercept compared to y(x)

• From 0 <x < 2, g(x) has a faster rate of change.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Function A is linear and starts with $1000 and increases by $100 each day y=100x+1000. Function B is exponential and begins with $20 but doubles each day y = 20(2)^x. On which interval (domain) does Function B exceed Function A?

• (0,1635.34)

• (0,6.353)

Function A is linear and starts with $1000 and increases by $100 each day y=100x+1000 Function B is exponential and begins with $20 but doubles each day y = 20(2)^x On which interval (domain) does Function B exceed Function A?

• (0,1635.34)

• (0,6.353)

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

Tags

CCSS.HSF.BF.B.3

Compare the following functions: Y(x) is shown in the table and f(x) = 95(1.25)^x Which statements are true? Show work (hint: make a table for f(x) and find the growth factor for y(x)).

• When x>3, f(x) will exceed y(x)

• g(x) will reach 120 first.

• f(x) has a smaller y intercept compared to y(x)

• From 0 <x < 2, g(x) has a faster rate of change.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

What is the equation of this table?

• y=512(1/4)^x

• y=32(4)^x

• y=32(1/4)^x

• y=512(4)^x

Tags

CCSS.HSF.LE.A.2