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Math Modeling and Application Flashcards

7 cards from real IAR practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 7 Math Modeling and Application flashcards as text

  1. A population of bacteria doubles every hour starting at 200. Which models the count P after h hours?

    Answer: P = 200(2)^h

    Doubling each hour is exponential growth with base 2 and starting value 200.

  2. A taxi charges $3.00 plus $2.50 per mile. A rider paid $18.00. How many miles was the trip?

    Answer: 6 miles

    Solving 3 + 2.5m = 18 gives 2.5m = 15, so m = 6 miles.

  3. A rectangular garden has length 3 feet more than its width w. Which models its area A?

    Answer: A = w(w + 3)

    Area is length times width, so A = w(w + 3).

  4. A savings account starts at $500 and grows by $25 each week. After how many weeks will it reach $750?

    Answer: 10 weeks

    Solving 500 + 25w = 750 gives 25w = 250, so w = 10 weeks.

  5. A map uses a scale of 1 inch = 25 miles. Two cities are 4.5 inches apart. What is the actual distance?

    Answer: 112.5 miles

    Multiply 4.5 inches by 25 miles per inch to get 112.5 miles.

  6. A company's profit is modeled by P = -2x^2 + 40x. What number of units x maximizes profit?

    Answer: 10 units

    The vertex is at x = -b/(2a) = -40/(2·−2) = 10 units.

  7. A class has a student-to-teacher ratio of 18 to 1. If there are 5 teachers, how many students are there?

    Answer: 90 students

    Multiply 18 students per teacher by 5 teachers to get 90 students.