Question

A student learned 100 Math formulae for an examination. The number of formulae the student can remember in '\(t\)' days after learning is given by \(f(t)=100(1-0.1t)^{2}\). Then, the magnitude of the rate at which the student forgets the formula 3 days after learning is:

• A. \(-14\)
• B. \(16\)
• C. \(14\)
• D. \(10\)

Hint:

Differentiate f(t) with respect to t, evaluate at t = 3 and take the magnitude.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
The rate at which the number of remembered formulae changes is \(f'(t)\). The rate of forgetting is its magnitude.

Step 2: Differentiate
\(f(t)=100(1-0.1t)^{2}\), so \(f'(t)=200(1-0.1t)(-0.1)=-20(1-0.1t)\).

Step 3: Evaluate at t = 3
\(f'(3)=-20(1-0.3)=-20\times 0.7=-14\).

Step 4: Magnitude
The student forgets at the rate \(|f'(3)|=14\) formulae per day.

Final Answer:
The magnitude of the rate of forgetting is 14 formulae per day. \[ \boxed{\text{(C) }14} \]