Question

The Barker family just left the local pet store with Lucky, their new family dog. The pet store owner told the Barker family that for the next 6 months, Lucky would grow at an average rate of 9 pounds per month. Currently, Lucky is 2 months old and weighs 3 pounds.


Age, in months 2 3 4 5 6 7 8
Weight, in pounds 3

Part A: Complete the given table that represents Lucky's current weight, in pounds, as a function of his age, in months.
Part B: Graph the data in the table from Part A. Be sure to label the graph and all data points.
Part C: Create a linear model that represents the Lucky's current weight, in pounds, as a function of his age, in months.
Part D: If Lucky continues to grow at the rate of 9 pounds per month beyond the expected six months, how much will Lucky weigh by the time he is one year old?

WRITER

Answer 1

Part A — completed table (age in months → weight in pounds)
- Age: 2 → 3
- Age: 3 → 12
- Age: 4 → 21
- Age: 5 → 30
- Age: 6 → 39
- Age: 7 → 48
- Age: 8 → 57

(Each month weight increases by 9 lb: weight at month n = 3 + 9*(n−2).)

Part B — graph instructions / description
- Horizontal axis: Age (months), label from 2 to 8.
- Vertical axis: Weight (pounds), label from 0 up to at least 60.
- Plot the points: (2,3), (3,12), (4,21), (5,30), (6,39), (7,48), (8,57).
- Connect the points with a straight line (they lie on a single line because growth is linear). Label the line or points “Lucky’s weight.”

Part C — linear model
- W(a) = 9a − 15, where a is age in months and W(a) is weight in pounds.
- Equivalent form: W(a) = 3 + 9(a − 2).

Part D — weight at one year (12 months)
- W(12) = 9(12) − 15 = 108 − 15 = 93 pounds.
- So Lucky would weigh 93 pounds at 12 months if the 9 lb/month rate continued.