P1) A population of rabbits oscillates 24 above and below an average of 88 durin
ID: 2920107 • Letter: P
Question
P1) A population of rabbits oscillates 24 above and below an average of 88 during the year, hitting the lowest value in January (t = 0). Find an equation for the population, P, in terms of the months since January, t. P2)What if the lowest value of the rabbit population occurred in April instead?P1) A population of rabbits oscillates 24 above and below an average of 88 during the year, hitting the lowest value in January (t = 0). Find an equation for the population, P, in terms of the months since January, t. P2)What if the lowest value of the rabbit population occurred in April instead?
P1) A population of rabbits oscillates 24 above and below an average of 88 during the year, hitting the lowest value in January (t = 0). Find an equation for the population, P, in terms of the months since January, t. P2)What if the lowest value of the rabbit population occurred in April instead?
Explanation / Answer
comparing with P(t)= Asin(B(t+C)) +k
k=88
A=24
period =12months
=>2/B = 12
=>B=/6
P(t)= 24sin((/6)(t+C)) +88
hitting the lowest value in January (t = 0). lowest value =88-24 = 64
P(0)=64
=>24sin((/6)(0+C)) +88=64
=>24sin((/6)(C)) = - 24
=>sin((/6)(C)) = - 1
=>((/6)(C)) = - (/2)
=>C = - 3
equation for population as a function of t (in months) is P(t)= (24*sin((/6)*(t-3))) +88
2)
if the lowest value of the rabbit population occurred in April . P(3)=64
=>24sin((/6)(3+C)) +88 =64
=>sin((/6)(3+C)) =-1
=>((/6)(3+C)) = - (/2)
=>3+C = - 3
=>C=-6
equation for population as a function of t (in months) is P(t)= (24*sin((/6)*(t-6))) +88
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