Unit 5 Assessment Review

Multiple Choice

Simplify the expression. Assume all variables are positive.

$$\left(x^5y^8\right)^5\cdot\sqrt[24]{x^{24}}$$

• $$x^{20}y^{30}$$

• $$x^{25}y^{35}$$

• $$x^{26}y^{40}$$

• $$x^{30}y^{45}$$

Multiple Choice

For the geometric sequence modeled in the table, the recursive rule is a₁ = 7 and a_n = .5(a_n-1) for n ≥ 2.

Identify the a₆ term of the geometric sequence.

• 0.4375

• 0.21875

• 2.1875

• 0.27864

Dropdown

Enter a, b, y-intercept, and the horizontal asymptote.

$$f\left(x\right)=-3\left(0.5\right)^x$$

a = ​

Select answer

b = ​

Select answer

y-intercept = (​

Select answer

,​

Select answer

)

The equation of the horizontal asymptote is ​

Select answer

Multiple Choice

Anakin was solving the following problem in class.

 

A certain germ doubles every 20 minutes. A population sample that begins with 300 cells in the testing tray can be represented by the function:  $$B=300\left(2\right)^t$$

where B is the number of bacteria cells and t is the time in 20 minute increments. 

 

Anakin graphed the function and described the y-intercept and asymptote of the function. Which of the following could be his description? 

• y-intercept = 150

  horizontal asymptote = 0

• y-intercept = 30

  horizontal asymptote = 2

• y-intercept = 300

  horizontal asymptote = 2

• y-intercept = 300

  horizontal asymptote = 0

Match

Match each verbal description to the function it represents.

• A family starts a savings account for emergencies. They started with $1500 and each year it increased by 4%.

• The value of a new truck decays at a rate of 10% each year. The value of the truck started at $60,000.

• The population of a small island in 2010 was 3000 and has decreased by 7% each year.

• $$f\left(x\right)=1500\left(1.04\right)^x$$

• $$f\left(x\right)=60000\left(0.90\right)^x$$

• $$f\left(x\right)=3000\left(0.93\right)^x$$

Dropdown

The table represents some points on the graph of an exponential function. Write the function that represents this relationship.



Choose the correct answer from each drop-down box to complete the function.

ƒ(x) = ​

Select answer

(​

Select answer

)^x

Dropdown

To find the quotient of powers, ​

Select answer

the exponents.



Simplify the exponents x²⁴∕x¹⁰ = ​

Select answer

Multiple Choice

Which of the following correctly identifies the domain and range of the following function $$f\left(x\right)=-12\left(5\right)^x$$ ?

• Domain: all real numbers

  Range: y>0

• Domain: all real numbers

  Range: y<0

• Domain: x>0

  Range: all real numbers

• Domain: all real numbers

  Range: all real numbers

Multiple Choice

The initial value of a home is $350,000. The value of the home will increase at a rate of 5% each year.

Which graph best models the situation?

Multiple Choice

Which expression is equivalent to $$17x^{-7}$$ for all values of y where the expression is defined.

• $$\frac{17}{x^7}$$

• $$\frac{17x}{x^7}$$

• $$10x$$

• $$\sqrt[7]{17x}$$