Apopulation of butterflies grow in such a way that each generation is simply 1.5 times the previous generation. there were 350 butterflies in the first generation, how many will there be by the 19th generation?

the formula is an= r* an-1

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.