IAR Math Modeling and Application 3 — Questions and Answers
Question 1: A population of bacteria doubles every hour starting at 200. Which models the count P after h hours?
- P = 200(2)^h (Correct answer)
- P = 200 + 2h
- P = 200(2h)
- P = 2(200)^h
Correct answer: P = 200(2)^h
Doubling each hour is exponential growth with base 2 and starting value 200.
Question 2: A taxi charges $3.00 plus $2.50 per mile. A rider paid $18.00. How many miles was the trip?
- 6 miles (Correct answer)
- 7 miles
- 5 miles
- 8 miles
Correct answer: 6 miles
Solving 3 + 2.5m = 18 gives 2.5m = 15, so m = 6 miles.
Question 3: A rectangular garden has length 3 feet more than its width w. Which models its area A?
- A = w(w + 3) (Correct answer)
- A = w + (w + 3)
- A = 2w + 3
- A = w^2 + 3
Correct answer: A = w(w + 3)
Area is length times width, so A = w(w + 3).
Question 4: A savings account starts at $500 and grows by $25 each week. After how many weeks will it reach $750?
- 10 weeks (Correct answer)
- 12 weeks
- 8 weeks
- 15 weeks
Correct answer: 10 weeks
Solving 500 + 25w = 750 gives 25w = 250, so w = 10 weeks.
Question 5: A map uses a scale of 1 inch = 25 miles. Two cities are 4.5 inches apart. What is the actual distance?
- 112.5 miles (Correct answer)
- 100 miles
- 125 miles
- 90 miles
Correct answer: 112.5 miles
Multiply 4.5 inches by 25 miles per inch to get 112.5 miles.
Question 6: A company's profit is modeled by P = -2x^2 + 40x. What number of units x maximizes profit?
- 10 units (Correct answer)
- 20 units
- 40 units
- 5 units
Correct answer: 10 units
The vertex is at x = -b/(2a) = -40/(2·−2) = 10 units.
Question 7: A class has a student-to-teacher ratio of 18 to 1. If there are 5 teachers, how many students are there?
- 90 students (Correct answer)
- 85 students
- 95 students
- 100 students
Correct answer: 90 students
Multiply 18 students per teacher by 5 teachers to get 90 students.
IAR Math Modeling and Application 3
A population of bacteria doubles every hour starting at 200.
Which models the count P after h hours?