AnswersSS4 PGCPS ALGEBRA 2 OC SUMMER 2027 - 793033Modeling with Functions

Modeling with Functions Answers

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Which type of function best models the data in the table below?xy244268110

Question illustration
A
inverse variation
B
linear
C
logarithmic
D
quadratic
2
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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?

A
The products of corresponding x- and y-values are equal.
B
The ratios of consecutive y-values are equal for evenly spaced x-values.
C
The y-values are the reciprocals of the corresponding x-values.
D
The change in y-values is constant for evenly spaced x-values.
3

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

Question illustration
A
y = x squared minus 8 x + 16
Option A
B
y = 5.5 x squared minus 0.5 x + 4
Option B
C
y = x squared + 4 x + 4
Option C
D
y = 2.5 x squared minus 0.5 x + 4
Option D
4

A new car sells for $25,000. The value of the car decreases by 15% each year. What is the approximate value of the car 5 years after it is purchased?

A
, or approximately $11,093
Option A
B
, or approximately $17,500
Option B
C
, or approximately $18,984
Option C
D
, or approximately $24,575
Option D
5

Tasha invests $5,000 at 6% annual interest and an additional $5,000 at 8% annual interest. Thomas invests $10,000 at 7% annual interest. Which statement accurately compares Tasha’s and Thomas’s investments if interest is compounded annually?Compound interest formula: t = years since initial depositn = number of times compounded per yearr = annual interest rate (as a decimal)P = initial (principal) investmentV(t) = value of investment after t years

Question illustration
A
Each person will have exactly the same amount over time because each invested $10,000 at an average interest rate of 7%.
B
Tasha’s investment will yield more over many years because the amount invested at 8% causes the overall total to increase faster.
C
Thomas’s investment will yield more from the start because he has more money invested at the average percentage rate.
D
Tasha’s investment will yield more at first because she invested some at a higher rate, but Thomas’s investment will yield more over the long run.
6

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?

A
, where l is the length, w is the width, and k is a constant ()
Option A
B
, where l is the length, w is the width, and m and b are constants
Option B
C
, where l is the length, w is the width, and k is a constant
Option C
D
, where l is the length, w is the width, and a is a constant
Option D
7

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?

Question illustration
A
,
Option A
B
,
Option B
C
,
Option C
D
,
Option D
8

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?

Question illustration
A
1.72 ft
B
3.05 ft
C
38.40 ft
D
46.08 ft
9

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?

A
an absolute value function since the values increase and then decrease
B
an exponential function since the ratios of the y-values are about the same
C
a linear function since the profit per person changes by $30 for each additional person
D
a quadratic function since the points lie on a curve that is symmetric about the line x = 30
10

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?

A
exponential
B
logarithmic
C
linear
D
quadratic

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