Question

A scientist has discovered an organism that replicates at a rate of five per hour and lives for one week. Each replicated organism also replicates at the same rate. At hour one, there is one organism. At hour two, there are five more organisms. How many total organisms are there at hour seven?

Answer 1

For every organism that replicates 5, there is a total of 6 at the next hour
So each hour the total multiplies by 6
\[N_t = 6 N_{t-1}\]
This forms a geometric series, the explicit formula is:
\[N_t = N_1 (6)^{t-1}\]
N1 = 1, plug in t = 7
\[N_7 = 6^6\]