Thread: derivative with words!

Bacteria in a culture increase at a rate proportional to the number present. An initial population of 200 triples in 10 hours. If this pattern of increase continues unabated, then the approximate number of bacteria after 1 full day is

I took 200 and multiply by 10 then multiply that with 12, but I got the wrong answer.

Two objects in motion from t=0 t=3 seconds have positions X lower case 1 (t)= cos (t^2+1) and x lower case 2(t)= e^t/2t. How many times during the 3 seconds do the objects have the same velocity?

I know you suppose to take the derivative but do something with it.

The velocity of a particle in motion along a line (for t=>0) is v(t)=ln(2-t^2). Find the acceleration when the object is at rest.

I took the derivative, so -2t/2-t^2, but I don't know what to do next.

Bacteria in a culture increase at a rate proportional to the number present. An initial population of 200 triples in 10 hours. If this pattern of increase continues unabated, then the approximate number of bacteria after 1 full day is?

take time as measured in hours.

You are told that the population satisfies the differential equation:



for some constant .

hence:



Put and we get:



Also we have:



so:



Now evaluate .

CB