Discrete Math

[Guest]

As a scientist who was doing research on a newly found bacteria, you investigated the growth rate of the bacteria hourly. With a1, a2, a3, a4 representing the population of the bacteria after the 1st hour until 4th hour, your investigation revealed that the population of the bacteria was 100(1), 100(8), 100(27), 100(64) per um2.

Assume a_n represents the bacteria’s population size after n hour. Determine the formula of a_n.


What is the population size of the bacteria after 10 hours?


What is the summation of population size after 50 hours?

[shyamjayakannan]

from the 4 values given, [tex]a_n=100n^3/\mu m^2[/tex]. After 10h, [tex]a_{10}=100\times10^3=10000/\mu m^2[/tex].

Summation up to 50h = [tex]\sum_{i=1}^{50}100i^3=100\left\{\frac{50(50+1)}{2}\right\}^2=162562500[/tex]