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:
 $y = 1 * (2) ^{( \frac{1}{30}x)}$
 By the time the sample weighs 583.8 g, we have:
 $583.8 = 1 * (2) ^ {( \frac{1}{30}x)}$
 From here, we clear x:
 $log2 ((2) ^ {(\frac{1}{30} x)}) = log2 (583.8)$
 $\frac{1}{30}x = log2 (583.8)$
 $x = 30 * log2 (583.8) x = 276 minutes$
 Answer:
 the sample will weight 583.8 g at 276 minutes