Question

The data displayed by the bar graph can be described by the mathematical model4xp=5 + 24 where x is the number of years after 1980 and p is the percentage of college freshmen in a certain area who had anaverage grade of Ain high school. Use this information to answer parts (a) and (b) below.

Answer 1

Part a) The idea here is to know how precise is our model in respect of the graph. What says the formula about 2010? Well, from 1980 to 2010, there are 30 years; the formula thus says that the percentage of college freshmen with an average of A is

`p(30)=(4\cdot30)/(5)+24=48\text{ \%}`

This is not the value the graph gives, which is 49%. Because

`48\text{ \%}<49\text{ \%}`

we say that the model underestimates the value displayed by the graph. The actual value is (again) 49%.

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Part b) The idea here is to "shift gears", and given a value of p (in this case 64%) obtain a value of x. That replacement in the model gives us

`64=(4\cdot x)/(5)+24`

Let us solve it for x:

`64-24=(4x)/(5)`
`40=(4x)/(5)`
`40\cdot5=4x`
`200=4x`
`50=(200)/(4)=x`

Then, the prediction is that in the year 2030 (1980+50) approximately 64% of college freshmen will have had an average grade of A...