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    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!
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    (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
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    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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