A scientist has discovered an organism that produces five offspring exactly one hour after its own birth, and then goes on to live for one week without producing any additional offspring. 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?

Question

Rascal

Mathematics

5 September, 14:56

A scientist has discovered an organism that produces five offspring exactly one hour after its own birth, and then goes on to live for one week without producing any additional offspring. 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?

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Answers (2)

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Finnegan Porter · Answer 1

Finnegan Porter 5 September, 15:17

0

19,531 is the right answer

Kallie Sims · Answer 2

19531

Step-by-step explanation:

At hour 1, there is 1 organism.

At hour 2, there is 1 + 5 organisms.

At hour 3, there is 1 + 5 + 25 organisms.

We can model this as the sum of a geometric series, where the first term is 1 and the common ratio is 5.

S = ∑ 1 (5) ^ (n-1)

The sum of the first 7 terms is:

S = a₁ (1 - rⁿ) / (1 - r)

S = 1 (1 - 5⁷) / (1 - 5)

S = 19,531