a scientist has discovered an organism that produces five offspring exactly one hour after its own birth…

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?\no 2,801\no 19,531\no 19,607\no 97,655

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?\no 2,801\no 19,531\no 19,607\no 97,655

Answer

Answer:

B. 19,531

Explanation:

Step1: Identify the sequence type

This is a geometric - sequence problem. The first - term (a_1 = 1), and the common ratio (r = 5).

Step2: Determine the number of terms

We start at hour 1 and want to find the total number of organisms at hour 7. The number of terms (n=7).

Step3: Use the sum formula for a geometric sequence

The sum formula for a geometric sequence is (S_n=\frac{a_1(r^n - 1)}{r - 1}) when (r\neq1). Here, (a_1 = 1), (r = 5), and (n = 7). [S_7=\frac{1\times(5^7-1)}{5 - 1}]

Step4: Calculate (5^7)

(5^7=5\times5\times5\times5\times5\times5\times5 = 78125).

Step5: Calculate the numerator

(5^7-1=78125 - 1=78124).

Step6: Calculate the sum

(S_7=\frac{78124}{4}=19531).