Ascientist has discovered an organism that produces five offspring exactly one hour after its own birth, and then goes on to live 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

Correct
Option B: 19531

Solution:
At hour 1 there is only 1 organism.
This organism gives birth to 5 offspring at hour 2.
Each of these 5 give birth to 5 offspring, resulting in birth of 25 offspring at hour 3.
Likewise, 125 offspring are born at hour 4.

The number of organisms after each hour till the 7th hour will be:

1, 5, 25, 125, 625, 3125, 15625

Total number of organisms will be the sum of all the numbers. The sum can be counted manually by adding up these values. The sum comes out to be 19531.

The other way to find the sum is using the formula of Geometric Series. If we observe the numbers, after every hour, the number of offspring is increasing by 5. So first term of the series is 1 and common ratio is 5. We are to find the sum of 7 terms.

So sum will be:

The equation is y=17(7)+600 and it equals 717