NBT NBT Mathematical Modelling 5

Question 1

A swimming pool is being filled by two pipes. Pipe A fills the pool in 6 hours and Pipe B fills it in 4 hours. How long will it take to fill the pool if both pipes are open?

Accepted Answer

2.4 h

Answer

Combined rate = 1/6 + 1/4 = 5/12 pools per hour; time = 12/5 = 2.4 hours.

Question 2

A scientist models the cooling of a substance with T(t) = 20 + 80e^(−0.5t), where T is temperature (°C) and t is time (hours). What is the temperature at t = 0?

Accepted Answer

100°C

Answer

At t = 0, e^0 = 1, so T(0) = 20 + 80(1) = 100°C.

Question 3

A farmer encloses a rectangular plot using 120 feet of fencing, with one side against a barn (no fence needed). What width maximizes the enclosed area?

Accepted Answer

30 ft

Answer

With one side free, 2w + l = 120; Area = w(120 − 2w) is maximized at w = 30 ft.

Question 4

The value of a car depreciates by 15% each year. If the car initially costs $24,000, which expression gives its value after n years?

Accepted Answer

24000(0.85)ⁿ

Answer

Each year the car retains 85% of its value, so value = 24000(0.85)ⁿ.

Question 5

A company's profit P (in thousands) is modeled by P = −2x² + 20x − 30, where x is units sold (hundreds). How many units (in hundreds) maximizes profit?

Accepted Answer

5

Answer

Vertex at x = −20/(2×−2) = 5; so 500 units maximizes profit.

(NBT) National Benchmark Test Practice Test

(NBT) National Benchmark Test Practice Test

NBT NBT Mathematical Modelling 5