NBT NBT Mathematical Modelling 4

Question 1

A car rental company charges a flat fee of $25 plus $0.15 per mile. Which equation models the total cost C for m miles?

Accepted Answer

C = 0.15m + 25

Answer

The flat fee is a constant ($25) and the per-mile charge is variable, giving C = 0.15m + 25.

Question 2

A population of bacteria doubles every 3 hours. If the initial population is 500, what is the population after 9 hours?

Accepted Answer

4000

Answer

After 9 hours there are 9/3 = 3 doubling periods, so population = 500 × 2³ = 4000.

Question 3

A water tank holds 800 gallons and drains at 40 gallons per hour. Which inequality represents when the tank has more than 200 gallons remaining?

Accepted Answer

800 − 40t > 200

Answer

The remaining volume is 800 − 40t and it must exceed 200, giving 800 − 40t > 200.

Question 4

A projectile is launched upward with height modeled by h(t) = −16t² + 64t + 5. What is the maximum height reached?

Accepted Answer

69 ft

Answer

The vertex occurs at t = −64/(2×−16) = 2; h(2) = −16(4) + 64(2) + 5 = −64 + 128 + 5 = 69 ft.

Question 5

A store marks up wholesale prices by 40% and then applies a 10% discount for members. If the wholesale price is $50, what is the member price?

Accepted Answer

$63.00

Answer

Marked-up price = $50 × 1.40 = $70; member price = $70 × 0.90 = $63.

(NBT) National Benchmark Test Practice Test