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# dP/dt Integration watch

1. I'm fine with integration, but I've never been given a question on our homework thats set out with dP/dt for example. I think I've got part a) somewhere, but have no clue how to do b). Would appreciate it if anyone helped a bit

"Rate of increase of a population of bacteria in a sandwich is given by; dP/dt=4-root t. P is population in thousands and t is time elapsed in hours.

a) Given there are initially 1000 bacteria in the sandwich, find an expression for P in terms of t.

b) What time does the number of bacteria reach a maximum, and wthat is this value?"

For a) I think I got P=4t-2/3t^(3/2). But I'm not sure if correct or not. Also for b) I'm not sure as I've never come across a question like this.

Thanks again!
2. (Original post by jshep000)
I'm fine with integration, but I've never been given a question on our homework thats set out with dP/dt for example. I think I've got part a) somewhere, but have no clue how to do b). Would appreciate it if anyone helped a bit

"Rate of increase of a population of bacteria in a sandwich is given by; dP/dt=4-root t. P is population in thousands and t is time elapsed in hours.

a) Given there are initially 1000 bacteria in the sandwich, find an expression for P in terms of t.

b) What time does the number of bacteria reach a maximum, and wthat is this value?"

For a) I think I got P=4t-2/3t^(3/2). But I'm not sure if correct or not. Also for b) I'm not sure as I've never come across a question like this.

Thanks again!
For (a) you need the constant of integration ... You will then use P=1000, t=0 to find the value of c

For (b) you know that you get a max or a min when the differential equals 0
3. Not sure why you messaged rather than posting here

When I said that you needed the constant of integration I mean that your answer for (a) should have +c on the end ... Then you need to find c

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