The amount of bacteria in a petri dish increases at a rate proportional to the amount present. At time t=0, the amount of bacteria in the dish is 10 grams. At time t=2, the amount of bacteria in the dish is 30 grams. What is the amount of bacteria in the dish at time t=6?

Question

Mathematics

Marina Day

31 May, 17:53

The amount of bacteria in a petri dish increases at a rate proportional to the amount present. At time t=0, the amount of bacteria in the dish is 10 grams. At time t=2, the amount of bacteria in the dish is 30 grams. What is the amount of bacteria in the dish at time t=6?

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Ramiro Reese · Answer 1

Step-by-step explanation:

Formula to be used is N=N0e^ (kt)

N0 - amount of bacteria at time 0, which is 10g

t=2, 30g

30 = 10*e^ (k*2)

3 = e^ (2k)

2k = ln3

k = 0.5ln3

At t=6:

N = 10*e^ (0.5ln3*6)

N = 10e^ (3ln3)

N = 10e^ln27

N = 10*27 = 270

So the amount of bacteria at t=6 is 270