Answer
a) $-96$
b) underestimates the average yearly decrease by $-34$
Work Step by Step
a) Using the formula $$f(x)=1.1x^3-35x^2+264x+557$$ we can determine the values
$f(7)=1067.3$ and
$f(12)=585.8$.
Therefore, by inserting it into the slope formula $$m=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}=\frac{585.8-1067.3}{12-7}\approx-96$$
b) Because the average yearly decrease determined in Exercise $28$ was $-130$ and the result obtained using the slope was $-96$, it follows that the slope from part $(b)$ underestimates the average yearly increase determined in exercise 28 by $-130-(-96)=-34$.
