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?

A.2,801
B.19,531
C.19,607
D.97,655

Answer 1

At hour one, there is 1 organism. At hour two, there is five more organism. At hour three. there will be 6 x 5 = 30 more organisms, etc

This is a geometric sequence with a = 1 (i.e. number of organisms at hour one), r = 5 (number of reprications per hour).

The total number of organisms at hour seven is the sum of the first seven terms of the sequence given by a(r^n - 1)/(r - 1) = 1(5^7 - 1)/(5 - 1) = (78125 - 1)/4 = 78124/4 = 19,531