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how to find something initially decreases and then the smallest number of something Watch

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    hey, i'm doing a question and im on the final part. I have just found a model which relates population with time.

    equations are:
    Original: P=600e^kt
    refined mode: dp/dt=P(0.005-0.008cos(0.02t))
    new refined model: P=600e^(0.005t - 0.4 sin(0.02t)

    'show that, according to the refined model, the number of ladybirds will decrease intially, and find the smallest number for ladybirds in the greenhouse'

    and a table of values is given:
    t=0, P=600
    t=150, P=1200
    t=250, P=3100


    how would i go about answering this question? (my teacher suggested putting dp/dt=0, solving to find t and subbing that value in but not sure how?
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    This is a differential equation question and the data represent conditions to allow you to find the constants of integration. These are separable equations but you need to quote the original question if you want help.

    What board and which exam (year and unit) is this?
 
 
 
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