c D www.webassign netweb/Student/Assignment-Responsessubmindep 5673511 This exer

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c D www.webassign netweb/Student/Assignment-Responsessubmindep 5673511 This exercise uses the population growth model. The count in a culture of bacteria was 400 aner 2 hours and 2seoo aner 6 hours. your answer the nearest whole number) (a) what is the relative rate of growth of the bacteria populatan? Express your answer as entage (Round to (b) What was the initial size of the outure? (Round your answer to the nearest whole number X bacteria (c) Find a function that models the number of bacteria non aner t hours. (Enter your answer in the form noen, Round your nJ value to the nearest whole number. Round your r value to two decimal places.) nearest hundred, (d) Find the number of bacteria after 4-5 hours. (Round your answer to the X bacteria After how many hours will the number or bacteria reach sa ooo? Round your answer to two deelmai places.) Need Help? LA L Submit Answer Save Progress Practice Another Vornion

Explanation / Answer

(2 hrs , 400) and (6hrs , 25600)

N = noe^kt

400 = noe^2k   ; 25600 = noe^6k

Divide both : 64 = e^4k

Take natural log on both sides: ln(64) = 4k

k =1.039 ; k = 103.9 %

So, equation can be written : N = noe^1.039t

400 = noe^2.039

no = 400/e^2.039 = 50 (intial amount)

N(t) = 50e^1.029t

at t= 4.5 hrs no. of bacteria : N(4.5) = 50e^(1.029*4.5) = 5128

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