$2)$ Based on data from $1988$ through $2003,$ the poverty rate in the U$.$S$.$can beapproximated by

p$($x$)=0\mathrm{.}092$x$2-8\mathrm{.}1$x$+190$percentage points $(38<=$x$<=44)$

where x is the U$.$S$.$ median household income in thousands of dollars.

a$)$ Find the average rate of change for each interval which shows the average rate ofchange of p over successive intervals of length $0\mathrm{.}5$ and create the table for givenintervals. Make sure you label the columns for the table. Intervals $[39,39\mathrm{.}5],[39\mathrm{.}5,40],[40,40\mathrm{.}5],[40\mathrm{.}5,41],[41,41\mathrm{.}5],[41\mathrm{.}5,42]$

b$)$ Interpret your answer for the interval$[40,40\mathrm{.}5],$ being sure to indicate the directionof change and the units of measurement.

c$)$ As the median household income rises, what happens to the poverty rate?