the doctor took the temperature of a dead body at 11.30 P.M., which was 94.6⁰ F. He took the temperature of the body again after one hour, which was 93.4⁰ F. If the temperature of the room was 70⁰ F, estimate the time of death. taking normal temperature of human body = 98.6⁰ F.

The velocity v of mass, of a rocket at time t, is given by the equation: \(m\frac { dv }{ dt } +V\frac { dm }{ dt } =0,\)Where 'V' is the constant velocity of emission. If the rocket starts from when t = 0 with mass m, prove that : \(v=Vlog\left( \frac { { m }_{ 0 } }{ m } \right) .\) Should we encourage rocket technology, why?

It is given that the rate at which some bacteria multiply is proportional to the instantaneous number present. If the original number of bacteria doubles in two hours, in how will it be five times?

In a culture,the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria proportional to the number present?

The rate of increases in the number of bacteria in a certain culture is proportional to the number present. Given that the number triples in 5 hours, find how many bacteria will be present after 10 hours. Also, find the time necessary of bacteria to be 10 times the number initially present.\(\left( { log }_{ e }3=1.0986,{ e }^{ 2.1972 }=9 \right) \)  (approx.)