Algebra Benchmark 2 Review

An apple tree produces 𝟓𝟎𝟎 pounds of apples in the year 𝟐𝟎𝟏𝟕 and produces an average of 𝟏𝟎% fewer pounds of apples each following year. The input-output table shows two values of a geometric sequence, where the input represents the time, in years, since 𝟐𝟎𝟏𝟕, and the output represents the pounds of apples that the tree produces.

Which function, 𝒇(𝒏), models the situation, where 𝒏 represents an integer greater than 𝟎?

A cell phone battery has a charge of 𝟎% when the cell phone is plugged into a charger. The table of the function 𝒇(𝒕) models the cell phone’s battery percentage 𝒕 minutes after the cell phone is plugged into the charger.

Which statement is true about the function on the interval from 𝒕=𝟐𝟎 to 𝒕=𝟖𝟎?

• The average rate of change on the interval is 1.25, representing an average increase of 1.25% per minute.

• The average rate of change on the interval is 1.25, representing an average increase of 1% every 1.25 minutes.

• The average rate of change on the interval is 0.80, representing an average increase of 1% every 0.80 minute.

• The average rate of change on the interval is 0.80, representing an average increase of 0.80% per minute.

Two students represent the values, in dollars, of their coin collections with linear functions, where 𝒙 is the time in years since the coin collections were started.

If 𝒙≥𝟎, which statement is true?

• The function representing the value of Student 1’s coin collection has a greater slope than the function representing the value of Student 2’s coin collection.

• The function representing the value of Student 1’s coin collection has a greater 𝑦-intercept than the function representing the value of Student 2’s coin collection.

• The function representing the value of Student 1’s coin collection has a smaller slope than the function representing the value of Student 2’s coin collection.

• The function representing the value of Student 1’s coin collection has a smaller 𝑦-intercept than the function representing the value of Student 2’s coin collection.

A ceramic potter sells coffee mugs at a craft festival for a profit. The input-output table shows several values of an arithmetic sequence, where the input represents the number of mugs sold, and the output represents the profit, in dollars.

Which function, 𝒇(𝒏), models the situation, where 𝒏 represents an integer greater than 𝟎?

Which table of values shows 𝒚 as a function of 𝒙?

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The table shows the number of miles a runner has remaining, 𝒇(𝒙), in a marathon after 𝒙 hours since beginning the marathon.

What is the average rate of change from hour 𝟏 to hour 𝟒?

• −18 miles per hour

• −6 miles per hour

• 6 miles per hour

• 18 miles per hour

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• slope and the change in the total amount of rain, in inches per hour

• slope and the initial amount of rain, in inches, at midnight

• 𝑦-intercept and the change in the total amount of rain, in inches per hour

• 𝑦-intercept and the initial amount of rain, in inches, at midnight

Water is drained at a constant rate of 𝟐 gallons per minute from a fish tank containing 𝟐𝟖 gallons of water. Which equation represents the number of gallons of water remaining in the tank, 𝒚, based on the number of minutes, 𝒕, since water started draining from the fish tank, where 𝟎≤𝒕≤𝟏𝟒?