Final answer:
The function modeling the baby's weight as a function of age in months is W(t) = 0.5t + 7.5. The baby weighed 10.4 pounds at about 5.8 months old, and at 6.2 months old, the baby weighs 10.6 pounds. The linear function's slope indicates a consistent monthly weight gain.
Step-by-step explanation:
The student has asked to find a linear function to model the baby’s weight. To create the function W(t) where 'W' is the weight of the baby in pounds and 't' is the age of the baby in months, we use the initial weight as the y-intercept and the monthly weight gain as the slope in the linear equation W(t) = mt + b.
a) The initial weight (b) is 7.5 pounds, and the weight gain (m) is 0.5 pounds/month. The linear function is W(t) = 0.5t + 7.5.
b) A reasonable domain for the function is 0 ≤ t ≤ 12 since we're only looking at the first year. A reasonable range would be 7.5 ≤ W ≤ 12 since the baby could not weigh less than the birth weight and will gain 0.5 pounds for each of the 12 months, resulting in a maximum weight of 12 pounds.
c) If the function is graphed, the x-intercept would be where W(t)=0, which is not reasonable for this function as the weight cannot be 0. The y-intercept is when t=0 and the weight is at its initial value of 7.5 pounds.
d) The slope of the function is 0.5, which represents a steady monthly weight gain of half a pound.
e) To find when the baby weighed 10.4 pounds, we solve for t: 10.4 = 0.5t + 7.5, resulting in t = 5.8. The baby weighed 10.4 pounds at approximately 5.8 months old.
f) If the input is 6.2, we plug it into the function: W(6.2) = 0.5(6.2) + 7.5 = 10.6. The baby weighs 10.6 pounds at 6.2 months old.