1. A savings account earns simple interest according to the equation $A = 1000 + 50t$, where $A$ is the amount in dollars and $t$ is the number of years. How much interest is earned after 5 years?
2. A plant grows at a constant rate of 2 cm per day. If the plant is initially 5 cm tall, which equation models the height $h$ of the plant after $d$ days?
3. A phone plan charges $$\25$$ per month plus $$\0.10$$ per text message. Which variable represents the number of text messages in the equation $y = 0.10x + 25$?
4. A train travels at a constant speed of 80 kilometers per hour. How far will it travel in 3.5 hours?
5. A hot air balloon is descending at a rate of 5 meters per minute. If its initial altitude is 200 meters, what equation models the altitude $y$ after $x$ minutes?
6. The cost of manufacturing a product is given by the equation $C = 500 + 3x$, where $C$ is the total cost in dollars and $x$ is the number of units produced. What is the fixed cost in this context?
7. A plant is 6 inches tall when it is purchased and grows at a constant rate of 1.5 inches per week. Let $x$ be the number of weeks since purchase and let $y$ be the plant's height (in inches). Which equation best models the relationship?
8. A candle burns down at a constant rate. It is 18 cm tall at time $x=0$ hours and 12 cm tall at time $x=3$ hours. If $x$ is time (hours) and $y$ is height (cm), which equation best models the candle's height over time?
9. A runner's distance from the starting line increases at a constant rate. The relationship is modeled by $y = 0.25x$, where $x$ is time in seconds and $y$ is distance in meters. What is the meaning of the slope in this context?
10. A gym charges a one-time sign-up fee and then a monthly fee. The total cost after $x$ months is $y = 30x + 80$, where $x$ is months and $y$ is total cost (dollars).
What is the meaning of the <u>slope</u> in this context?
11. A ball is thrown upward from a platform. Its height (in meters) after $x$ seconds is modeled by $y = -5x^2 + 20x + 2$. Which part of the equation represents the initial height of the ball at time $x=0$?
12. A student earns money by tutoring. The relationship between hours tutored $x$ and total earnings $y$ (in dollars) is modeled by $y = 18x + 25$.
Based on the model $y = mx + b$, what is the predicted value of $y$ when $x = 6$? Show the substitution: $y = 18(6) + 25$.
13. A cyclist rides at a constant speed and covers 10 miles in 0.5 hours. Which equation represents the distance $d$ in miles traveled in $t$ hours?
14. A gym charges a $$\50$$ monthly fee and $$\10$$ per class attended. Which equation represents the total monthly cost $T$ for attending $c$ classes?
15. A store sells notebooks for a fixed price each. The relationship between the number of notebooks $x$ and the total cost $y$ is shown below.
| Notebooks $x$ | Cost $y$ (dollars) |
|---:|---:|
| 2 | 5 |
| 6 | 15 |
| 10 | 25 |
Which equation best models the relationship between $x$ and $y$?
16. A construction project is expected to cost $C = 20000 + 150t$, where $C$ is the total cost in dollars and $t$ is the time in days. What does the slope represent in this situation?
17. A cell phone plan has a monthly fee of $$\40$$ and charges $$\0.05$$ per text message. Which equation models the total monthly cost $C$ for $t$ text messages?
18. Which equation best represents the relationship between the number of books $b$ and the total cost $c$ if each book costs $15?
19. A phone company offers a service plan that charges a base fee of $$\30$$ per month plus $$\0.10$$ per minute of call time. What is the meaning of the slope in this context?
20. A taxi company charges a base fare of $$\3$$ plus $$\2$$ per mile. Which equation best models the relationship between the total fare $y$ and the number of miles $x$ traveled?
21. A phone plan’s total cost is modeled by $y = 45 + 0.08x$, where $x$ is the number of text messages sent in a month and $y$ is the total monthly cost in dollars.
Which variable represents the number of text messages?
22. A fitness trainer charges an initial fee of $$\50$$ plus $$\10$$ per session. Which equation represents the total cost $C$ for $n$ sessions?
23. A water tank is being filled at a constant rate. The amount of water is modeled by $y = 7x + 15$, where $x$ is time in minutes and $y$ is the amount of water in liters.
According to the model, how many liters of water are in the tank after $x = 9$ minutes?
24. A taxi ride has a fixed starting fee plus a constant cost per mile. The total cost is modeled by $y = 2.50x + 4$, where $x$ is the number of miles and $y$ is the total cost in dollars.
What is the meaning of the <u>y-intercept</u> in this context?
25. A student saves money each week. The amount saved is modeled by $y = 15x + 5$, where $x$ is the number of weeks and $y$ is the total amount saved in dollars.
According to the model, how much money will the student have saved after $8$ weeks?
26. The profits of a company are given by the equation $P = 5000 + 200x$, where $P$ is the profit in dollars and $x$ is the number of units sold. What is the profit from selling 10 units?
27. A biologist is tracking the population of a certain species of fish in a lake. The initial population is $P\_0$, and the population grows at a constant rate of $5\text{%}$ per year. 
Which of the following functions $P(t)$ best models the population $t$ years after the initial observation?
28. A radioactive isotope decays such that its mass, $M(t)$, in grams, after $t$ days is modeled by $M(t) = 50(0.5)^{\frac{t}{8}}$. What is the mass, in grams, of the isotope after 24 days?
29. A boat travels downstream and covers 40 miles in 2 hours. What is the boat's speed in miles per hour?
30. A car rental company charges a flat fee of $$\30$$ plus $$\0.25$$ per mile driven. What is the meaning of the slope in the equation that models this scenario?
31. A company sells widgets for $$\5$$ each. Which equation represents the total revenue $R$ from selling $n$ widgets?
32. The equation $S = 300 - 20t$ models the speed of a car, where $S$ is the speed in km/h and $t$ is the time in hours. What is the speed after 3 hours?
33. A ferry service charges $$\15$$ per passenger plus a flat fee of $$\100$$ per trip. Which equation represents the total cost $T$ for $p$ passengers?
34. A gym charges a one-time sign-up fee and a monthly membership fee. The total cost after $x$ months is modeled by $y = 25x + 40$, where $y$ is the total cost in dollars.
What is the meaning of the $y$-intercept in this context?
35. A scuba diver descends at a constant rate. The depth is modeled by $y = 4x$, where $x$ is time in minutes and $y$ is depth in meters.
According to the model, how deep is the diver after $7.5$ minutes?
36. A water tank is being filled at a constant rate. It contains 50 liters at time $x=0$ minutes and 170 liters at time $x=6$ minutes. Let $x$ be time in minutes and $y$ be the amount of water in liters.
Which equation best models the relationship between $x$ and $y$?
37. A taxi fare is modeled by $y = 2.25x + 4.50$, where $x$ is the number of miles traveled and $y$ is the total fare in dollars.
What does the slope represent in this context?
38. The number of bacteria in a dish doubles every hour. At hour 0 there are 200 bacteria. Let $x$ be the number of hours and $y$ be the number of bacteria.
Which equation best models this relationship?
39. A delivery service charges according to the linear model $y = 3.5x + 6$, where $x$ is the number of miles driven and $y$ is the total charge in dollars.
Based on the model, what is the predicted charge when $x = 10$ miles? (Substitute into $y = 3.5x + 6$.)
40. The temperature $y$ (in °C) in a freezer changes linearly with time $x$ (in minutes). It is $20$°C at $x=0$ and $-4$°C at $x=12$.
Which equation best models the relationship between $x$ and $y$?
41. A concert venue sells tickets. The total revenue is modeled by $y = 30x$, where $x$ is the number of tickets sold and $y$ is revenue in dollars.
What does the slope represent in this context?
42. A printing company charges according to $y = 0.12x + 15$, where $x$ is the number of pages printed and $y$ is the total cost in dollars.
What is the meaning of the $15$ in this model?
43. The equation $E = 50t + 1000$ models the energy consumption of a factory, where $E$ is the energy used in kilowatt-hours and $t$ is the number of hours of operation. What is the meaning of the y-intercept in this context?
44. The cost of producing an item is given by the equation $C = 100 + 5x$, where $C$ is the cost in dollars and $x$ is the number of items produced. What is the cost for producing 20 items?
45. The equation $H = 180 - 10d$ models the height of a candle in centimeters, where $H$ is the height and $d$ is the number of days it has been burning. What is the height after 12 days?
46. The population of a city is modeled by the equation $P = 100000 + 1200t$, where $P$ is the population and $t$ is the number of years since 2010. What is the population in 2020?
47. The equation $Y = 1000 + 200f$ models the yield of a crop, where $Y$ is the yield in kilograms and $f$ is the number of fertilizers used. What is the yield with 5 fertilizers?
48. A cell phone plan costs $$\30$$ per month plus $$\0.15$$ per text message. Which equation represents the total monthly cost $C$ for sending $t$ text messages?
49. The sales of a product are predicted by the equation $S = 200 + 15d$, where $S$ is the number of units sold and $d$ is the number of days. What is the predicted sales after 10 days?
50. The temperature on a winter day is modeled by the equation $T = -3h + 12$, where $T$ is the temperature in degrees Celsius and $h$ is the number of hours since midnight. What is the temperature at 5 AM?
51. A gym charges a one-time sign-up fee plus a monthly membership cost. In the equation $y = 25x + 40$, $x$ is the number of months and $y$ is the total cost (in dollars). What is the meaning of the $y$-intercept in this context?
52. A delivery service charges a flat fee of $$\10$$ plus $$\2$$ per kilometer driven. Which equation models the total cost $C$ for a delivery of $k$ kilometers?
53. A plant’s height increases by the same amount each week. It is 12 cm tall at week 0 and 27 cm tall at week 5. Let $x$ be the number of weeks and $y$ be the height in centimeters.
Which equation best models the relationship between $x$ and $y$?
54. A storage tank is being filled with water at a constant rate of 10 gallons per minute. If the tank starts at 100 gallons, what is the equation for the amount of water $w$ in the tank after $t$ minutes?
55. A garden hose dispenses water at a rate of 15 liters per minute. If the hose has dispensed 60 liters of water, how many minutes has it been running?
56. The function $B = 800 - 5n$ models the number of books in a library, where $B$ is the number of books and $n$ is the number of days books are borrowed. How many books are left after 50 days?
57. A taxi company charges a flat rate of $$\2$$ plus $$\1.25$$ per mile driven. Which equation represents the total cost $C$ for a trip of $m$ miles?
58. The cost of attending a concert is modeled by the equation $C = 25n + 5$, where $C$ is the total cost in dollars and $n$ is the number of tickets. What is the cost for 3 tickets?
59. A ball is thrown upward from a height of 5 meters. Its height after $x$ seconds is modeled by the quadratic equation $y = -4x^2 + 12x + 5$, where $y$ is height in meters.
According to the model, what is the height of the ball after $2$ seconds?
60. A bacteria culture starts with 50 bacteria and doubles every hour. Let $x$ be the number of hours and $y$ be the number of bacteria. Which equation best models this relationship?
61. A biologist is tracking the population of a certain species of fish in a lake. The initial population is $P\_0$, and the population grows at a constant rate of $5\text{%}$ per year. 
Which of the following functions $P(t)$ best models the population $t$ years after the initial observation?