Answer: Hello there!
We know that in the first generation there are 350 butterflies.
then in the second generation, there will be 1.5*350 = 525 butterflies, and so on.
the third generation you have 1.5*(1.5*350) = 788 butterflies
you can see the pattern here, each generation after the first one, you add another 1.5 to the multiplication:
The equation that describes the growth of the population as a function of the generations n, is the next one:
P(n) = 350*1.5^(n -1)
now, the if n = 19, we have:
p(19) = 350*1.5^(19 - 1) = 350*1.5^(18) = 517262.15
but you can't have a 0.15 of a butterfly, you need a whole number, then we need to round it.
The first number after the decimal point is a 1, so we need to round down the population:
The population of butterflies in the 19th generation is equal to 517262 butterflies.