Question 8037 – GATE 2016 [Set-1]

In a process, the number of cycles to failure decrease exponentially with an increase in load.
General exponential function = a⋅e^-bx
i.e., No. of cycles to failure = a⋅e^-bx
load = x
At a load of 80 units, it takes 100 cycles to failure.
So, no. of cycles to failure = 100
load = 80
i.e., 100 = a⋅e ^{– b(80)} ——–(1)
When the load is halved, it takes 10000 cycles to failure.
No. of cycles to failure = 10,000
load = 40
i.e., 10,000 = a⋅e ^{– b(40)} ———(2)

No. of cycles to failure = 5,000
load = x?
i.e., 5000 = a⋅e ^{– bx}
Multiply with 2 on both sides,
10,000 = 2⋅a⋅e ^{– bx} ——- (4)