Multiple Choice

1. A company's profits, $P$ (in thousands of dollars), $t$ years after its founding can be modeled by a linear equation. In its third year, the profit was $\$120,000$. In its seventh year, the profit was $\$180,000$. What was the company's estimated profit (in thousands of dollars) in its first year of operation?

   $75$

   $15$

   $45$

   $90$

2. A hot air balloon starts its descent from an altitude of $A$ meters. Its altitude decreases at a constant rate of $15$ meters per minute. If the balloon reaches the ground after $20$ minutes, which equation models the balloon's altitude $h$ (in meters) after $t$ minutes?

   $h = -15t + 20$

   $h = 15t + 300$

   $h = 15t - 300$

   $h = -15t + 300$

3. Company A charges a flat fee of $\$50$ plus $\$0.10$ per minute for a consultation. Company B charges no flat fee but $\$0.25$ per minute. For how many minutes of consultation will the total cost be the same for both companies?

   $333.33$ minutes

   $100$ minutes

   $200$ minutes

   $500$ minutes

4. A reservoir currently holds $15,000$ cubic meters of water. It is being drained at a constant rate of $2.5$ liters per second. How many days will it take for the reservoir to be completely empty? ($1$ cubic meter $= 1000$ liters)

   $173.61$ days

   $150$ days

   $6000$ days

   $69.44$ days

5. A car's fuel tank initially holds $60$ liters of fuel. It consumes fuel at a rate of $8$ liters per $100$ kilometers driven. Which statement correctly describes the domain for the number of kilometers, $d$, the car can travel before running out of fuel, assuming a continuous linear model?

   $d \ge 0$

   $0 \le d \le 750$

   $d \le 750$

   $0 \le d \le 60$

6. A farmer observes that the height of his corn plants increases by $3$ inches every $2$ weeks during the growing season. When he first measured them, they were $1$ foot tall. If the growing season lasts $18$ weeks, what is the expected height of the corn plants (in feet) at the end of the season?

   $13$ feet

   $2.25$ feet

   $3.25$ feet

   $39$ feet

7. A small business starts with a revenue of $5,000$ in its first month. Its monthly revenue increases by a constant amount of $750$ each subsequent month. In which month will its monthly revenue first exceed $20,000$?

   $21$st month

   $22$nd month

   $20$th month

   $27$th month

8. A swimming pool is being filled with water. When the filling process started, there were $200$ liters of water in it. Water is added at a constant rate of $k$ liters per minute. After $45$ minutes, the pool contains $3,800$ liters. If the pool has a maximum capacity of $5,000$ liters, how much longer (in minutes) will it take to fill the pool completely from $3,800$ liters?

   $15$ minutes

   $17.5$ minutes

   $20$ minutes

   $62.5$ minutes

9. Two delivery trucks, Truck A and Truck B, leave a depot at the same time and travel in opposite directions. Truck A travels at a constant speed of $80$ km/h. Truck B travels at a constant speed of $95$ km/h. How many hours will it take for the trucks to be $1050$ km apart?

   $6$ hours

   $7$ hours

   $13$ hours

   $5$ hours

10. The value $V$ (in dollars) of a certain piece of machinery depreciates linearly over time $t$ (in years). Its initial value is $\$120,000$. After $5$ years, its value is $\$70,000$. What does the x-intercept of the linear model represent in this context?

    The value of the machinery after $1$ year.

    The number of years until the machinery has no value.

    The initial value of the machinery.

    The annual depreciation rate.

11. A restaurant uses a specific coffee blend. They start the day with $5$ kg of coffee beans. Each cup of coffee requires $15$ grams of beans. If the restaurant makes $30$ cups per hour, how many hours will it take to use all the coffee beans?

    $16.67$ hours

    $2.5$ hours

    $11.11$ hours

    $3.33$ hours

12. A factory manufactures two types of widgets: Type A and Type B. Production costs for Type A are $\$5$ per widget plus a fixed daily overhead. Production costs for Type B are $\$8$ per widget plus the same fixed daily overhead. On a day when $100$ Type A widgets and $50$ Type B widgets were produced, the total cost was $\$1150$. If, on another day, $80$ Type A widgets and $120$ Type B widgets were produced, what would be the total cost?

    $1360$

    $1610$

    $1710$

    $1050$

13. A rare comic book was purchased for $\$500$ and is expected to increase in value by a constant amount each year. After $10$ years, its value is $150\%$ of its original price. What will be its value after $15$ years?

    $750$

    $1250$

    $925$

    $875$

14. The number of available parking spaces, $P$, in a lot is a linear function of the number of cars, $C$, that have entered the lot. Initially, there were $200$ available spaces. After $40$ cars entered, there were $160$ available spaces. What is the slope of the linear equation that models this situation, and what does it represent?

    $200$; It represents the initial number of parking spaces.

    $1$; It represents that for every car that enters, one parking space becomes available.

    $-1$; It represents that for every car that enters, one parking space becomes unavailable.

    $-40$; It represents the total decrease in spaces after $40$ cars.

15. A T-shirt printing business has a fixed monthly cost of $\$800$. Each T-shirt costs $\$7$ to produce and sells for $\$15$. How many T-shirts must the business sell in a month to make a profit of exactly $\$1000$?

    $200$ T-shirts

    $225$ T-shirts

    $125$ T-shirts

    $100$ T-shirts

16. A particular type of bacteria population grows at a constant rate. At $9:00$ AM, there were $500$ bacteria. At $1:00$ PM on the same day, the population had grown to $1100$ bacteria. Assuming linear growth, what was the estimated population at $7:00$ AM that day?

    $200$ bacteria

    $50$ bacteria

    $350$ bacteria

    $425$ bacteria

17. A caterer charges a flat fee of $\$200$ for an event, plus $\$25$ per guest. The venue has a maximum capacity of $150$ guests, and a minimum booking of $30$ guests is required. Which inequality represents the possible total cost, $C$, for an event?

    $950 \le C \le 3950$

    $30 \le C \le 150$

    $200 \le C \le 3950$

    $750 \le C \le 3750$

18. A scientist is tracking the decomposition of a sample. The mass of the sample, $M$ (in grams), decreases linearly over time $t$ (in hours). Initially, the sample had a mass of $120$ grams. After $3$ hours, its mass was $105$ grams. How long (in hours) will it take for the sample to reach a mass of $60$ grams?

    $18$ hours

    $15$ hours

    $9$ hours

    $12$ hours

19. Two small towns, Town A and Town B, are tracking their populations. Town A currently has $8,000$ residents and is growing by $200$ residents per year. Town B currently has $12,000$ residents and is declining by $100$ residents per year. In how many years will the populations of the two towns be equal?

    $13.33$ years

    $10$ years

    $40$ years

    $20$ years

20. A plumber charges a call-out fee plus an hourly rate. For a $2$-hour job, he charged $\$190$. For a $4.5$-hour job, he charged $\$340$. What is his call-out fee (in dollars)?

    $70$

    $60$

    $120$

    $50$