# The function P(x)= -0.008x2 + 0.815x-9.983 models the percentage of the U.S population whose age is xthat have earned an advanced degree. (more than a bachelors degree)in march 2003. A) What is the age for which the highest percentage of Americans have earned an advanced degree? What is the highestpercentage? B) Is the percentage of Americans who have earned an advanceddegree increasing or decreasing for individuals between the ages of40 and 50.

The function $P\left(x\right)=-0.008{x}^{2}+0.815x-9.983$
models the percentage of the U.S population whose age is xthat have earned an advanced degree. (more than a bachelors degree)in march 2003.
A) What is the age for which the highest percentage ofAmericans have earned an advanced degree? What is the highestpercentage?
B) Is the percentage of Americans who have earned an advanceddegree increasing or decreasing for individuals between the ages of40 and 50.
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Monica Dennis
First step is to find the derivitive of the function
p'(x)=-0.016x+0.815
Next find where the derivitive is equal to 0.
0.016x=0.815
x=50.9375
The above is the age for which the highest percentage of americanshave earned an advanced degree to find the number we plug it backinto the original equation and get 10.774031
###### Not exactly what you’re looking for?
A) The age with the highest advanced degree % will occur at the topof the parabola (the maximum). This occurs at an age of50.94 and a percentage of 10.77.
B) Since the parabola is increasing before age 50, the percentage of americans with advanced degrees is increasing between 40 and 50.