Linear Functions: Profit, Cost, and Growth Transformations

1. A company produces x units of a product, and the profit can be modeled by the equation P(x) = 3(2x + 5). What is the profit when 10 units are produced?

• 90

• 100

• 75

• 60

2. The height of a plant over time can be modeled by the equation H(t) = 2(3t + 4). If t represents weeks, how tall will the plant be after 6 weeks?

• 30

• 50

• 36

• 44

3. A car rental company charges a base fee of $20 plus $15 for each day rented, modeled by C(d) = 15(d + 1). What is the total cost for renting the car for 5 days?

• $75

• $90

• $100

• $60

4. The temperature in a city can be modeled by T(h) = 4(2h - 3) + 10, where h is the number of hours since sunrise. What is the temperature 5 hours after sunrise?

• 38

• 45

• 25

• 30

5. A gym charges a monthly fee of $30 plus $10 for each class attended, represented by G(c) = 10c + 30. If a member attends 8 classes, what is their total cost?

• 130

• 90

• 150

• 110

6. The distance a cyclist travels can be modeled by D(t) = 5(2t + 1), where t is the time in hours. How far will the cyclist travel in 3 hours?

• 35

• 25

• 40

• 30

7. A store's revenue can be modeled by R(x) = 4(3x + 2). If the store sells 5 items, what is the total revenue?

• 50

• 68

• 60

• 72

8. The number of visitors to a park can be modeled by V(d) = 2(4d + 1), where d is the number of days. How many visitors will there be after 7 days?

• 68

• 48

• 58

• 78

9. A delivery service charges a flat rate of $25 plus $5 for each package delivered, modeled by D(p) = 5p + 25. What is the total charge for delivering 10 packages?

• $75

• $50

• $90

• $100

10. A farmer's crop yield can be modeled by Y(x) = 6(2x + 1). If the farmer plants 4 acres, what will be the yield?

• 54

• 72

• 60

• 48