Let's assume that you're being asked to write a formula for the dog's weight.
In this case, w = (weight after x months) = (initial weight) (1 + r)^x
We know the initial and final weights: 2 lb and 110 lb. We also know that the time period involved is 8 months. What is the "consistent" rate at which the dog gains weight?
110 lb = (2 lb) (1 + r)^8
Let's solve this for r.
Dividing both sides by 2 lb, 55 = (1 + r)^8
Finding the 8th root of both sides: 1.65 = 1 + r
Solving for r, r = 0.65
The dog gains weight at the consistent rate of 0.65 lb/month.
Check: Does (2 lb) (1.65)^8 come out to 110 lb?
(2 lb)(54.94) = 109.9 lb (very close indeed to 110 lb).
