NBT Mathematical Modelling Flashcards

A stone is dropped from a bridge. Its distance fallen (in metres) after t seconds is d = 4.9t². How far has it fallen after 3 seconds?

Answer: 44.1 m

d = 4.9(3)² = 4.9 × 9 = 44.1 metres. The model d = 4.9t² represents free fall under gravity (½g ≈ 4.9 m/s²).

A phone battery starts at 100% and loses charge linearly, reaching 20% after 8 hours. What is the equation for the battery percentage B after t hours?

Answer: B = -10t + 100

Rate of loss = (100 - 20)/8 = 80/8 = 10% per hour. B = 100 - 10t or B = -10t + 100. Both options A and B represent the same equation.

In South Africa, the exchange rate is approximately R18.50 to 1 USD. If an item costs $85, what is the cost in rands?

Answer: R1 572.50

Cost in rands = 85 × 18.50 = R1 572.50. Currency conversion multiplies the foreign amount by the exchange rate.

A water tank drains at a rate proportional to the amount remaining. If it starts with 800 litres and loses 10% per hour, how much remains after 3 hours?

Answer: 583.2 litres

After each hour, 90% remains: 800(0.9)³ = 800 × 0.729 = 583.2 litres. Exponential decay retains 90% each hour.

A company finds that the cost C of producing x items is C = 500 + 8x. The revenue R from selling x items is R = 20x. How many items must be sold to make a profit?

Answer: More than 42

Profit when R > C: 20x > 500 + 8x → 12x > 500 → x > 41.67. Since x must be a whole number, at least 42 items must be sold.

A loan of R50 000 is taken at 12% per annum simple interest. What is the total amount owed after 4 years?

Answer: R74 000

Simple interest: I = Prt = 50 000 × 0.12 × 4 = R24 000. Total = 50 000 + 24 000 = R74 000. Simple interest is calculated on the original principal only.