Question

a scientist has discovered an organism that produces five offspring exactly one hour after its own birth, and the 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? 2,801 19,531 19,607 97,655

Explanation:

Step1: Identify the growth - pattern

This is a geometric - growth problem. The initial number of organisms $a_1 = 1$ at hour 1, and the common ratio $r = 5$ since each organism produces 5 offspring per hour.

Step2: Use the formula for the nth term of a geometric sequence

The formula for the nth term of a geometric sequence is $a_n=a_1\times r^{n - 1}$, where $n$ is the number of terms, $a_1$ is the first - term, and $r$ is the common ratio. Here, we want to find the number of organisms at hour 7, so $n = 7$, $a_1 = 1$, and $r = 5$.

Step3: Calculate the number of organisms

Substitute the values into the formula: $a_7=1\times5^{7 - 1}=5^6$.
$5^6=5\times5\times5\times5\times5\times5 = 15625$.

Answer:

15625