Problem
David bought a puppy and has been tracking its weight at the end of each month since it was born. He was told by the dog's breeder that the dog should have an adult weight somewhere between 45 and 50 pounds. \begin{tabular}{|c|c|} \hline End of Month & Weight (in pounds) \\ \hline 1 & 4 \\ \hline 2 & 9 \\ \hline 3 & 15 \\ \hline 4 & 18 \\ \hline 5 & 21 \\ \hline 6 & 23 \\ \hline 7 & 25 \\ \hline 8 & 31 \\ \hline 9 & 33 \\ \hline 10 & 38 \\ \hline 11 & 43 \\ \hline 12 & 46 \\ \hline \end{tabular} The quadratic function $w(t)=0.012 t^{2}+3.467 t+2.318$ models the weight of the puppy after $t$ months. By this model, what is the interpolated weight of the dog after 5.5 months? Round your answer to the nearest pound. Answer pounds
Solution
Step 1 ：Given the quadratic function \(w(t)=0.012 t^{2}+3.467 t+2.318\) which models the weight of the puppy after \(t\) months, we are asked to find the interpolated weight of the dog after 5.5 months. This requires substituting \(t=5.5\) into the function and rounding the result to the nearest pound.
Step 2 ：Substitute \(t=5.5\) into the function to get \(w = 21.7495\).
Step 3 ：Round \(w = 21.7495\) to the nearest pound to get \(w = 22\).
Step 4 ：Final Answer: The interpolated weight of the dog after 5.5 months is \(\boxed{22}\) pounds.
