Question

The following geometric sequences represent the population of two bacterial cultures at the 1 hour mark the 2 hour mark the 3 hour mark and so on

culture A starts with more bacteria but culture b has a ratio of increase that is larger which culture will have the greater population at the 18 hour mark

Answer 1

\[A = A_{0}(r)^{t}\]

where A0 is the initial population, A is the final population, r is the common ratio, and t is time (years)

to find r for a sequence, simply take any value in the sequence and divide it by the previous value

find r for both cultures A and B

then, using the common ratio r, and the initial value A0 for each culture, let t = 18 and plug these values into the formula to find the final population A