How do I replace an old x for a new x 80 times automatically?

Question

To put in in different terms, here is what I am trying to find out:

1 old x required to make 1.5 new x

all old x's must die

80 generations

Start at 2

I made the equation of (x*1.5), but still need to find out how to replace each generation so that it automatically does this:

(2*1.5)=3

(3*1.5)=4.5

(4.5*1.5)=6.75

(6.75*1.5)=10.125

(10.125*1.5)=15.1875

(15.1875*1.5)=22.78125

(22.78125*1.5)=34.171875

(34.171875*1.5)=51.2578125

HOW DO I DO THIS AUTOMATICALLY???

Answer 1

Hey, what you described is an example of exponential growth. Let me show you a pattern in what you're describing:

Gen 1: (2*1.5)=3

Gen 2: (3*1.5)= (2*1.5)*1.5 = 2 * (1.5)² = 4.5

Gen 3: (4.5*1.5) = 2 * (1.5)² * 1.5 = 2 * (1.5)³ = 6.75

At generation n, the size is of the form 2(1.5)². So if you want it when n = 80, do 2(1.5)⁸⁰