The GATE Grind

GATE 2016 CE (CE1) – Question 10

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for failure. The load for which the failure will happen in 5000 cycles is ________.

  1. 40.00
  2. 46.02
  3. 60.01
  4. 92.02

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) 46.02

Explanation

Write N=A exp(−kL). The observations give10000/100=exp(40k), so k=ln100/40. Since5000 is half the count at40, the required increment is ln2/k=6.0206. Thus L=46.02, matching **B**; linear interpolation is inappropriate for exponential decay.