Topic 6 Review - Exponential Functions

Topic 6 Review Exponential Functions

6-1A

Solving Exponential Equations

Multiple Choice

What is the first step in solving the following exponential equation?

 $\left(3^{2x+1}\right)\left(3^{-x+4}\right)=3^{10}$  

• Set the exponenents equal to each other

• Use the Product of Powers Property to add the exponents

• Change the bases

• Cancel out the exponents

Multiple Choice

Okay, exponents added. What is the next step to solve this exponential equation?

 $3^{x+5}=3^{10}$  

• Change the bases

• Divide both sides by 3

• Set the exponent equal to each other.

6-1B

Solving Exponential Equations

Multiple Choice

What is the first step in solving the follow exponential equation?

 $2^{6x}=8^{x+1}$  

• Change the base of 8 to  $2^3$  

• Change the base of 2 to  $2^3$  

• Set the exponents equal to each other

• Add the exponents together

Multiple Choice

What is the next step to solving the exponential equation?

 $2^{6x}=\left(2^3\right)^{x+1}$  

• Use the Power of a Power Property and multiply the exponents

• Set the exponents equal to each other

• Divide by 2 on each side

Fill in the Blanks

Finish solving the exponential equation to find the value of x.

 $2^{6x}=2^{3x+3}$  

6-2

Exponential Functions

Multiple Choice

Which equation below is an exponential?

• $$y=mx+b$$

• $$y=2x^2$$

• $$y=a\left(b\right)^x$$

• $$y=\sqrt{x}$$

Multiple Choice

In the equation  $$y=a\left(b\right)^x$$    what does the "a" represent?

• Common Ratio

• Slope

• Y-Intercept

• Common Difference

Multiple Choice

In the equation  $y=a\left(b\right)^x$    what does the "b" represent?

• Common Ratio

• Slope

• Y-Intercept

• Common Difference

Multiple Choice

Ms. Slominski inherited a rare hockey puck collection from her mother. It initially had 10 hockey pucks. Ms. Slominski keeps doubling the collection each year. Which exponential function represents Ms. Slominski's hockey puck collection size.

• $$y=10\left(\frac{1}{2}\right)^x$$

• $$y=2\left(10\right)^x$$

• $$y=10\left(\frac{1}{2}\right)^x$$

• $$y=10\left(2\right)^x$$

Multiple Choice

What is the y-intercept in an exponential function

$$y=a\left(b\right)^x$$  

• y > 0

• (0, a)

• y = 0

• All Real Numbers

Multiple Choice

What is the domain of an exponential function

$$y=a\left(b\right)^x$$  

• y > 0

• (0, a)

• y = 0

• All Real Numbers

Multiple Choice

What is the range of an exponential function

 $y=a\left(b\right)^x$  

• y > 0

• (0, a)

• y = 0

• All Real Numbers

Multiple Choice

What is the equation for the asymptote in an exponential function

 $y=a\left(b\right)^x$  

• y > 0

• (0, a)

• y = 0

• All Real Numbers

6-3A

Exponential Growth and Decay

Multiple Choice

You deposit $5,000 in a savings account. Each year your savings grows by 2%. Which exponential function below represents this scenario?

• $y=5000\left(1.2\right)^x$

• $y=5000\left(1.02\right)^x$

• $y=5000\left(.02\right)^x$

• $y=5000\left(.2\right)^x$

Multiple Choice

The population of a city starts at 30,000 but each year they lose 5% of their population. Which exponential equation represents this scenario?

• $y=30000\left(.5\right)^x$

• $y=30000\left(.05\right)^x$

• $y=30000\left(1.05\right)^x$

• $y=30000\left(.95\right)^x$

6-4

Geometric Sequences

Multiple Choice

What is the common ratio of the geometric sequence below:

$$48,\ 12,\ 3,\ \frac{3}{4},\ \frac{3}{16}$$  

• r = $$\frac{1}{4}$$  

• r = 4

• r = 48

• r = 0.75

Multiple Choice

Which explicit formula represents this Geometric sequence:

$$48,\ 12,\ 3,\ \frac{3}{4},\frac{3}{16}$$  

• $$a_n=\frac{1}{4}\left(48\right)^{n-1}$$  

• $$a_1=48$$   $$a_n=\frac{1}{4}\left(a_{n-1}\right)$$  

• $$a_n=48\left(\frac{1}{4}\right)^{n-1}$$  

• $$a_n=48\left(4\right)^{n-1}$$  

Multiple Choice

The population of germs in a petri dish is growing every day. If there are 150 germs on day 1, 225 on day 2, 337.5 on day 3, how many germs will there be on day 10? (Round to a whole number)

• 8,649

• 8,650

• 5,766

• 5,767

6-5

Transformations of Exponential Functions

Multiple Choice

Describe the transformation of the parent function

$$f\left(x\right)=6^x$$   to the function $$g\left(x\right)=6^{x-1}-3$$  

• Left 3 and Down 1

• Right 3 and Down 1

• Left 1 and Down 3

• Right 1 and Down 3

Multiple Choice

Which function represents a translation of 2 unit left and 2 units down of the parent function: $$f\left(x\right)=3^x$$  

• $$g\left(x\right)=3^{x-2}-2$$  

• $$g\left(x\right)=3^{x-2}+2$$  

• $$g\left(x\right)=3^{x+2}-2$$  

• $$g\left(x\right)=3^{x+2}+2$$