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An exponential growth/decay word problem. If spraying of grasshoppers

  1. Apr 8, 2009 #1

    HT3

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    1. The problem statement, all variables and given/known data
    If spraying of grasshoppers with 800kg/km^2 of a certain insecticide will kill 40% of these insects, how much insecticide is needed to kill 98% of the grasshoppers?
    (assume exponential relationship)

    2. Relevant equations
    [tex]\int[/tex]dP/dt=[tex]\int[/tex]kp
    lnP=kt+c
    e^(kt+c)=P


    3. The attempt at a solution
    I set up an equation relating the amount of insecticide to how many die (exp decay -k)
    800kg/km^2=Po(e^-k(.4))
    im unsure as where to go from here...or if im even on the right path
     
  2. jcsd
  3. Apr 8, 2009 #2
    insecticide is the input not the output.
    So,

    G_alive/G_intial = exp(-k.insecticide used)

    when insecticide used = 0 then G_alive/G_initial = 1 .. (no G killed)
     
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