Mortgage Rates The average 30-year fixed mortgage rate in the United States in the first week of May in 2010 through 2012 is approximated by
$M (t) = \frac{55.9}{t^{2} - 0.31 t + 11.2}$
percent per year. Here $t$ is measured in years, with $t = 0$ corresponding to the first week of May in 2010.+
(a) What was the average 30-year fixed mortgage rate in the first week of May in 2011 ( $t = 1$ )? (Round your answer to two decimal places.)
4.7
() $%$
(b) How fast was the 30-year fixed mortgage rate decreasing in the first week of May in 2011 ( $t = 1)$ ? (Round your answer to two decimal places.) 5600 $%$ per year

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Thus, the average 30-year fixed mortgage rate in the first week of May in 2011 was approximately $4.70 %$ .

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Step 1 ：The problem provides the function $M (t) = \frac{55.9}{t^{2} - 0.31 t + 11.2}$ percent per year, where $t$ is measured in years, with $t = 0$ corresponding to the first week of May in 2010.

Step 2 ：We are asked to find the average 30-year fixed mortgage rate in the first week of May in 2011, which corresponds to $t = 1$ in the given function.

Step 3 ：To find this, we substitute $t = 1$ into the function and calculate the result: $M (1) = 4.701429772918419$ .

Step 4 ：Rounding this to two decimal places, we get $4.70$ .

Step 5 ：Thus, the average 30-year fixed mortgage rate in the first week of May in 2011 was approximately $4.70 %$ .

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