Answer to Question #111594 in Mechanical Engineering for PRABHASH KUMAR JHA

Question

The % live bacteria due to sterilization follows an exponential relation such as % live = 30 exp (-0.01 T). T is the temperature in oC. What should be the
temperature to achieve just less than 5 % live bacteria?

Answer 1

Let A be the % live bacteria,

As per the question it is given as the % live bacteria is given as

$A=30 e^{-0.01T}$ ...........(i)

If it has to decrease 5% of live bacteria then temprature changes by

0.95 A= 30 $e^{-.01T_1}$ ....................(ii)

from (i) and (ii)

we get

0.95 = $e^{\frac{T}{T_1}}$

log(0.95)= $\frac{T}{T_1}$

T₁=- 44.90T So here temperature should be decrease by 44.90 ⁰C