The number of bacteria in a colony growing exponentially. At 4 pm yesterday the number of bacteria is 400.And at 6 pm yesterday it was 3600. How many bacteria in the colony at 7 pm?
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Answer:
10800
Step-by-step explanation:
The number of bacteria in a colony growing exponentially. At 4 pm yesterday the number of bacteria is 400.And at 6 pm yesterday it was 3600. How many bacteria in the colony at 7 pm?
Let say
B = B₀ Kⁿ
At 4 pm yesterday the number of bacteria is 400
B₀ = 400
n = number of hrs
at 6 pm yesterday it was 3600 => n = 6- 4 = 2 hrs
B₂ = 3600
=> 3600 = 400 * k²
=> k² = 9
=> k = 3
At 7 Pm Yesterday
n = 7-4 = 3
B₃ = 400 * 3³
=> B₃ = 27 * 400
=> B₃ = 10800
bacteria in the colony at 7 pm = 10800
or B₂ = 3600 & n = 7-6 = 1
Then B₃ = 3600 * 3¹ = 10800
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