IAR Math Modeling and Application 3

Question 1

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

Accepted Answer

P = 200(2)^h

Answer

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?

Accepted Answer

6 miles

Answer

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?

Accepted Answer

A = w(w + 3)

Answer

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?

Accepted Answer

10 weeks

Answer

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?

Accepted Answer

112.5 miles

Answer

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

IAR Practice Test