Question: Birthweight The rate of change of the percentage of low-birthweight babies (less than 5 pounds 8 ounces) in 2000 can be modeled by

\(P(w)=-11.5\left(0.86^{w}\right)\) percentage points per pound

when the mother gains \(w\) pounds during pregnancy. The model is valid for weight gains between 18 and 43 pounds. (Source: Based on data from National Vital Statistics Reports, vol. 50 , no. 5, February 12,2002 ,)

1. Sketch a graph of \(P\) from \(w=18\) to \(w=43\).
2. What does the fact that the graph of \(P\) lies below the \(t\) -axis from \(w=18\) to \(w=43\) tell you about the percentage of low-birthweight babies in $2000 ?$
3. Use five midpoint rectangles to estimate the area of the region between the graph of \(P\) and the \(w\) -axis from \(w=18\) to \(w=43 .\) Interpret your answer.

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