Question

A sample of bacteria has a doubling time of 30 minutes. if a student begins with 1 g of the bacteria, at what time will the sample weight 583.8 g

Answer 1

For this case we have a function of the form:

`y = A * (b) ^ x`
Where,
A: initial amount
b: growth rate
x: time in minutes
Substituting values we have:

`y = 1 * (2) ^{( (1)/(30)x)}`
By the time the sample weighs 583.8 g, we have:

`583.8 = 1 * (2) ^ {( (1)/(30)x)}`
From here, we clear x:

`log2 ((2) ^ {((1)/(30) x)}) = log2 (583.8)`

`(1)/(30)x = log2 (583.8)`

`x = 30 * log2 (583.8) x = 276 minutes`
Answer:
the sample will weight 583.8 g at 276 minutes