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

Modeling with Functions Answers

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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?

Question illustration
A
,
Option A
B
,
Option B
C
,
Option C
D
,
Option D
2
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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?

Question illustration
A
y = m x + b
Option A
B
y = a b Superscript x
Option B
C
y = a x squared + b x + c
Option C
D
, where
Option D
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 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
5

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
6

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?

Question illustration
A
atm
Option A
B
atm
Option B
C
0 atm
D
1 atm
7

The distance it takes a car to come to a complete stop after the brakes are applied is related to the speed that the car is traveling. The stopping distances and speeds are shown in the table below.Stopping Distance of a Car vs. SpeedStopping Distance, d (in feet)Speed, s (in miles per hour)2017.894025.306030.988035.7810040.00Which equation best represents the data in the table?

A
s = 4 StartRoot d EndRoot
Option A
B
s = 0.37 d + 20
Option B
C
s = 13.7log(d)
D
s = StartFraction 1 Over 25 EndFraction d squared
Option D
8

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
9

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.
10

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.

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