January 2019 Algebra 1 Regents, Parts III & IV

The following are some of the multiple questions from the August 2018 New York State Common Core Algebra I Regents exam.
The answers to Part I can be found here
The answers to Part II can be found here

August 2018 Algebra I, Part III

Each correct answer is worth up to 4 credits. Partial credit can be given. Work must be shown or explained.

33. Marilyn collects old dolls. She purchases a doll for $450. Research shows this doll's value will increase by 2.5% each year.
Write an equation that determines the value, V, of the doll t years after purchase.
Assuming the doll's rate of appreciation remains the same, will the doll's value be doubled in 20 years? Justify your reasoning.

Answer:
2.5% = 0.025, which gets added to 100% = 1.00.
So the equation is V = 450(1.025)^t
Substitute t = 20,
V = 450(1.025)²⁰ = 737.377... = $737.38
$450 * 2 = $900, so the doll will not double in value.
Also, (1.025)²⁰ is only 1.638... or 164%, which is less than double (200%).

34. The data given in the table below show some of the results of a study comparing the height of a certain breed of dog, based upon its mass.

Write the linear regression equation for these data, where x is the mass and y is the height. Round all values to the nearest tenth.
State the value of the correlation coefficient to the nearest tenth, and explain what it indicates.

Answer:
Place all the data into two lists in your graphing calculator and run a linear regression.
You should get a = 1.9 and b= 29.8, so y = 1.9x + 29.8.

Make sure you have DiagnosticsON, or you won't get r, the correlation coefficient.
r = .3, so it is a weak positive correlation.

Use this formula to find the value of V(3) and V(4) and subtract them to find the difference. (You can also graph this in your calculator and check the Table of Values)
V(3) - V(4) = 25000(0.815)⁴ - 25000(0.815)³
= 13533.584 - 11029.871 = 2503.713 = $2,503.71 depreciation between years 3 and 4.

35. Myranda received a movie gift card for $100 to her local theater. Matinee tickets cost $7.50 each and evening tickets cost $12.50 each.
If x represents the number of matinee tickets she could purchase, and y represents the number of evening tickets she could purchase, write an inequality that represents all the possible ways Myranda could spend her gift card on movies at the theater.
On the set of axes below, graph this inequality.

What is the maximum number of matinee tickets Myranda could purchase with her gift card? Explain your answer.

Answer:

13 movies. 13 is the highest whole number on the x-axis lower than the x-intercept. (13, 0) is in the solution set. (14, 0) is not.

36. One spring day, Elroy noted the time of day and the temperature, in degrees Fahrenheit. His findings are stated below.
At 6 a.m., the temperature was 50°F. For the next 4 hours, the temperature rose 3° per hour.
The next 6 hours, it rose 2° per hour.
The temperature then stayed steady until 6 p.m.
For the next 2 hours, the temperature dropped 1° per hour.
The temperature then dropped steadily until the temperature was 56°F at midnight.
On the set of axes below, graph Elroy's data.

State the entire time interval for which the temperature was increasing.
Determine the average rate of change, in degrees per hour, from 6:00 p.m. to midnight.

Answer:

The temperature is increasing on the graph between 6am and 4pm. (6am, 4pm)
At midnight (12) the temperature is 56. At 6pm, the temperature is 74.
Calculate the rate of change: (56 - 74) / (12 - 6) = -18 / 6 = -3 degrees per hour. The temperature is falling at an average rate of 3 degrees per hour. (If you write it the second way, "falling" implies the negative.)

August 2018 Algebra I, Part IV

A correct answer is worth up to 6 credits. Partial credit can be given. Work must be shown or explained.

37. A recreation center ordered a total of 15 tricycles and bicycles from a sporting goods store.
The number of wheels for all the tricycles and bicycles totaled 38.
Write a linear system of equations that models this scenario, where t represents the number of tricycles and b represents the number of bicycles ordered.
On the set of axes below, graph this system of equations.
Based on your graph of this scenario, could the recreation center have ordered 10 tricycles? Explain your reasoning.

Answer:

The equations that you want to graph are

t + b - 15
3t + 2b = 38
You could graph them this way, or rewrite them as
t = 15 - b
t = 38/3 - 2b/3
The slope of the first line is -1. The slope of the second line is -2/3.
You could graph them this way, or rewrite them as
b = 15 - t
b = 38/2 - 3b/2
The slope of the first line is -1. The slope of the second line is -3/2.
The two lines intersect at (8, 7), which is 8 tricycles and 7 bicycles.
Based on the graph, the recreation center could NOT have order 10 tricycles because t=10 is not the point of intersection. (They ordered 8.)

End of Exam

How did you do?

Questions, comments and corrections welcome.