Question

Hailey’s new puppy, Sparky, weighed 4 pounds at six weeks old. If the puppy gains 2.5 pounds each month, at how many months will Sparky weigh 14 pounds and is it modeled by a linear function or a exponential function

Answer 1

Assuming a month is 4 weeks, after x weeks, Sparky weighs

4 + (5/2)(x/4)

So, when do you have

4 + 5/8 x = 14

That is the number of weeks, not months. Clearly it is linear, not exponential. (2.5 lbs/month)

Answer 2

2.5 pounds/month is a constant slope of weight as a function of age.
Therefore we are dealing with a straight line, linear function.

(eventually it will hopefully turn exponential as it approaches full grown weight but that is a later problem :)

six weeks = 1.5 months
weight = weight at 1.5 months plus slope *time after 1.5 months
or
w = 4 + 2.5 (t - 1.5)
w = 2.5 t + 4 - 3.75
w = 2.5 t + .25 in slope intercept form

14 = 2.5 t + .25

2.5 t = 13.75

t = 5.5 months