A) What will be the formula for numbers N(t) of bacteria after "t" hours?
B) How many bacteria are in culture at the end of 10 hours?
Every hour, the amount is increased by 20%, meaning it's multiplied by 1.2
N(t) = N(initial)*((1.2)^t)
So every hour the number gets multiplied with an additional 1.2
When t = 10,
N(10) = 10000*((1.2)^10)
N(t) = N ∙ ( 1 + r )ᵗ
N = initial amount
r = growth rate
t = time elapsed
In this case:
N = 10,000
r = 20% = 20 / 100 = 0.2
N(t) = 10,000 ∙ ( 1 + 0.2 )ᵗ
N(t) = 10,000 ∙ 1.2 ᵗ
N(10) = 10,000 ∙ 1.2 ¹⁰ = 10,000 ∙ 1.2 ¹⁰ = 10,000 ∙ 6.1917364224 = 61,917.364224
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