Robin's family breeds Great Danes. In the last litter, one of the puppies grew at an unusually consistent rate. At birth, he weighed two pounds. At eight months, he weighed 110 pounds.

Accepted Solution

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).