A thermocouple behaves approximately as a first-order system. The element is initially at a temperature of 40°C and suddenly subjected to a temperature of 80°C. The thermocouple indicates a temperature 60°C after 3 s. How long will it take for the system to reach 99% of steady-state?

At 12 noon, the count in a bacteria culture was 400; at 4: 00 pm the count was 1200 let p(t) denote the bacteria cou population growth law. find: (a) an expression for the bacteria count at any time t (b) the bacteria count at 10 am. (c) the time required for the bacteria count to reach 1800.