Answer
a. $T(x)=41.78-0.19x$
b. year $ 2012$
Work Step by Step
a. Based on the given conditions, we can express the winning time as $T(x)=41.78-0.19x$, which gives $T(0)=41.78\ sec$ and an average rate of decrease of 0.19 second per year.
b. Let $T=35.7$, we have $41.78-0.19x=35.7$, which leads to $0.19x=6.08$ and $x=32$, corresponding to year $1980+32=2012$
