Answers PBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024Modeling with Exponential and Logarithmic Equations

Modeling with Exponential and Logarithmic Equations — Unit test Answers

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A travel agency made the table below to represent the profits it makes on a certain vacation package.Number of People vs. ProfitNumber of People Who Buy the Package, xProfit per Person (in dollars), y1050020800309004080050500Which of the following explains the best model for the data in the table?

an absolute value function since the values increase and then decrease

an exponential function since the ratios of the y-values are about the same

a linear function since the profit per person changes by $30 for each additional person

a quadratic function since the points lie on a curve that is symmetric about the line x = 30

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A science teacher wrote the table of values below.Amount of Hydrogen vs. pHAmount of Hydrogen, x(in moles per liter)pH, f(x)12345Which function models the data in the table?

Ramiro drew the graph below.Which equation represents the data in the graph?

y = x squared minus 8 x + 16

y = 5.5 x squared minus 0.5 x + 4

y = x squared + 4 x + 4

y = 2.5 x squared minus 0.5 x + 4

The time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation below., where l is the length of the pendulum in feetWhat is the approximate length of a pendulum that takes seconds to swing back and forth?

1.72 ft

3.05 ft

38.40 ft

46.08 ft

Janis was offered two different jobs when she graduated from college. She made the graph and table to show how much she would earn over time at each job.Earnings over Time for Job 1Earnings over Time for Job 2When will Janis’s salary be the same for job 1 and job 2, and how much will she be earning at that point?

The salaries will be the same in year 20, and she will be earning $80,000.

The salaries will be the same in year 16, and she will be earning $70,000.

The salaries will be the same in year 12, and she will be earning $60,000.

The salaries will be the same in year 10, and she will be earning $55,000.

The amount of water pressure exerted on a scuba diver varies with depth. The graph below shows the relationship between pressure, p, in atmospheres, and depth, d, in ft.Depth of Water and Water PressureBased on the information in the graph, what is the water pressure at sea level?

atm

0 atm

1 atm

The pressure of a fixed volume of a certain gas is related to its temperature as shown in the table below.Temperature of Gas vs. Pressure Temperature (in degrees Celsius)Pressure (in pascals)44915293609568977699Which type of function best models the data in the table?

exponential

logarithmic

linear

quadratic

Kareem wants to write an equation for the data in the table below.xy–3–2–101What is the general form of the equation Kareem can use to represent the data?

y = m x + b

y = a b Superscript x

y = a x squared + b x + c

, where

A rectangle with constant area has possible lengths and widths as shown in the table below. Width vs. Length of a RectangleWidth (w)Length (l)237.5418.75612.589.375Which equation can be used to find any corresponding length and width that fit the pattern in this table?

, where l is the length, w is the width, and k is a constant ()

, where l is the length, w is the width, and m and b are constants

, where l is the length, w is the width, and k is a constant

, where l is the length, w is the width, and a is a constant

Jordan uses a linear equation to model the data in a table. Which reasoning might Jordan have used in the decision to model the data with a linear equation?

The products of corresponding x- and y-values are equal.

The ratios of consecutive y-values are equal for evenly spaced x-values.

The y-values are the reciprocals of the corresponding x-values.

The change in y-values is constant for evenly spaced x-values.

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Modeling with Exponential and Logarithmic Equations — Unit test Answers

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