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Sagot :
The number of bacteria y in the culture after x hours will be y = 50(2)ˣ.
What is exponential growth ?
An exponential function faster and faster after every next value of the independent variable.
According to the given question the number of bacteria in a culture is increasing according to the law of exponential growth. after 3 hours, there are 400 bacteria, and after 6 hours, there are 3,200 bacteria.
We use the exponential growth equation y = arˣ where a is the initial value and r is common ratio and x represents time.
so 400=ar^3...(i) and 3200= ar^6...(i)
Dividing equation (ii) by equation (i) and solve for r we get r³ so r =2
substitute r into first equation 400=a(2)³
8a = 400.
a = 50.
∴ The no. of bacteria at any given time x will be. ( t is replaced by x)
y = 50(2)ˣ.
learn more about exponential growth here :
https://brainly.com/question/11487261
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