Equation on a straight line

Question

I have the below maths problem - may someone give me a hint?

I have an equation modelling the dog's weight with respect to its age. The model is from the age of 20 weeks to the age of 48 weeks.

My question is the following: "Explain why the model cannot be extended to model accurately the dog's weight at birth."

Thanks

The equation given is $w = 0.92\,t - 0.15$

Answer 1

It depends on your assumptions, clearly, the weight of the dog may or may not be directly proportional to its age. Thus, modeling it on a straight line may not be possible if we are to model the actual situation. But, with proper assumption that the weight increase with age. Then, it's plausible.

Answer 2

If your equation is $W=ma+c$, where $W$ is weight, $a$ is age, and $m$ and $c$ are constants, then let $a=0$ to find the weight at birth. Presumably the answer to the question is that your value $c\leq 0$, which gives a weight at birth $\leq 0$, which is impossible.

Answer 3

Without numbers it's theoretically possible and there is no theoretical reason it can't be extrapulated in theory.

But we know puppies tend to be very small at birth an go through a rapid weight gain in the first few weeks. But week $20$ the puppy is several times heavier than it was at birth. In fact it's nearly full grown! The growth rate from $20$ weeks to $48$ weeks is nowhere near as great. $48$ weeks is nearly a year and by that time the dog has be full grown for months.

The growth a dog goes through from $4.5$ months to $11$ months is only a tiny fraction of what it grew from $0$ months to $4.5$ months which is less time.

If a dog is $\frac 23$ grown by $20$ weeks and completely grown in $48$ weeks, then the dog will be over $\frac 13$ grown at birth. Which is absurd.

Consider this: https://pets.thenest.com/growth-weight-border-collies-9435.html

Newborn border collies are tiny, compact packages of organs, skin and bones. With a birthweight of 7 to 14 ounces, border collies are smack in the middle of the birthweight range for medium-sized breeds. Every puppy gains weight at a different rate, but each puppy should gain weight steadily. While a puppy may lose water weight the first 24 hours, a healthy puppy immediately begins putting on weight after that point. Within the first week, border collie puppies double their birthweight and for every week after that until 6 weeks of age, they gain 1/2 to 1 1/2 ounces a day.

Puppy

At 6 weeks of age, your 3- to 6-pound border collie has more than quadrupled his birthweight already. During puppyhood, your highly active critter will gain about 2 to 4 pounds a week until roughly 14 weeks of age. Around that point, the extremely rapid weight gain levels off and your pooch will gain about a pound a week until he's 6 months old. Remember, though, that every puppy is an individual and gains weight at a slightly different rate.

So by my calculations a border collie will weigh $14$ oz. at birth. And $6$ weeks will weigh $3$ pounds. And $14$ weeks will weigh $31$ pounds. At $20$ weeks it will weigh $37$ lbs. And at $6$ months ($26$ weeks) it will weigh $43$ lbs. And and $48$ weeks it will weigh $43$ lbs.

So And $20$ weeks it weighs $37$ lbs and at $48$ it weighs $43$. If I linearly extrapolate I that $6$ lbs gained in $28$ weeks or $\frac {3}{14}$ lbs a week. So I calculate at birth it must have weighed $37 - 20\times \frac {3}{14} = 32.7$ lbs.

I am WAY off!