Algebra 1: STAAR Exponentials, Sequences and Other Types Review

Which expression is equivalent to   $$\frac{x^{-5}y^4}{x^2y}$$ for all values of x and y where the expression is defined?

Write a simplified expression for

  $$\frac{x^{-8}y^6}{x^{ }y^3}$$

for all values of x and y where the expression is defined?

Make sure all the exponents are positive.

Write a simplified expression for

  $$\left(\frac{2x^2}{3y^3}\right)^3$$

for all values of x and y where the expression is defined?

Make sure all the exponents are positive.

A sample of a substance with an initial mass of 500 grams is decreasing 32% per hour. 

Create a function that can be used to find y, the mass of the substance in grams remaining after x hours.

Enter your answer in the space provided.

In the expression shown,  $$x$$  is a value where the expression is defined.

$$(2x^5)(3x^{-2})^2$$

What is the simplest form of the expression? Write your answer in the form $$ax^b$$ .

Enter your answer in the box provided.

The graph shows the number of game consoles sold in millions since 2009.

Based on this information, which function best models the number of game consoles sold in millions $$x$$ years since 2009?

Laboratory technicians recorded the population of a species of bacteria each hour for 7 hours. The population in hours after $$x$$ hours can be modeled by the exponential function $$f\left(x\right)=575\left(1+0.40\right)^x$$ .

Choose the correct answer from each drop-down menus to complete the statements.

The initial population of bacteria when the technicians began recording was ​ (a)   .

The population is ​ (b)   at a rate of ​ (c)   each hour.​

A sequence can be generated by using the equation shown, where $$a_1=-2$$ and  $$n$$  is a whole number greater than 1.

$$a_n=8+a_{\left(n-1\right)}$$

What are the first four terms in the sequence?

A shipping company started with 108 employees. The number of employees at the shipping company decreases at a rate of 7.5% each year.

Which function can be used to model the number of employees, f(x), at the shipping company after x years?

Which expression is equivalent to   $$\frac{x^{-5}y^4}{x^2y}$$ for all values of x and y where the expression is defined?