The population of bacteria in a culture grows at a rate proportional to the numb

Question

The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. After 3 hours it is observed that 600 bacteria are present. After 10 hours 2000 bacteria are present. What was the initial number of bacteria? (Round your answer to the nearest integer.) A thermometer is taken from an inside room to the outside, where the air temperature is 25 degree F. After 1 minute the thermometer reads 75 degree F, and after 5 minutes it reads 50 degree F. What is the initial temperature of the inside room? (Round your answer to two decimal places.) A tank contains 120 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 4 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.

Explanation / Answer

3) Bacteria grows exponentially!! Hence B(t) = B0. eat where a = growth rate.

    2000 = b0. e10a, 600 = bo.e3a . Solving, a = .171 and bo = 359 ( could be 360 depending on exact e value)

5) Rate of change of Salt Level = Rate of Inflow - Rate of Outflow = 4 - A(t)/120*4 =4 - A(t)/30

A'(t) = 4 - A(t)/30

   

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