I am currently in 8th grade and in my Algebra class we are currently covering exponential growth, e.g. bacteria splitting, fruit fly growth, etc. Anyway, one exercise we did was on zombies. The problem started with 5 "sleeper cell" zombies, who each day could "turn" three humans. The equation looked like this: $5\times 3^x = h$ 

$h$ = humans infected each day.

While this was interesting, I wanted to see how many *total* infected humans there were *including* the original 5 "sleeper cell" zombies. I had a scientific calculator on hand so I calculated the sum of all of this with $\displaystyle \sum\_{d=0}^{19}5(3)^d$ where $d = $ days passed. 

This ended up being 8,716,961,000, a little more than the total Earth's population. Therefore $d>18$ but $d<19$ in order for the sum to $\approx$ 7,000,000,000 (Earth's population).

My question is, is it possible to solve for the stopping point of the sum/upper value of the sum? Please keep in mind that although I am in AP 8th grade math, I'm no mathematician, so please keep the explanations within the realm of my comprehension.