a Subtract the expression for P from the expression for N.
B
b Subtract to find the number of years since 2000. Then, substitute that value into the equation from Part A.
A
a S=0.55t^2-0.05t+3.7
B
b 3030
Practice makes perfect
a We are given two equations that represent the number of students enrolled in a school system. To find the equation for the number of students in the upper grades S, we will subtract the equations for the number of primary school students P from the total number of students N.
The equation that models the number of students S in grades 6 through 12 is as follows.
S= 0.55t^2 - 0.05t + 3.7
b We want to find the number of students who were enrolled in grades 6 through 12 in 2007. We can use the equation from Part A and substitute a value for t. Since t represents the number of years since 2000, we first need to find the number of years between 2000 and 2007.
2007-2000=7Now we can substitute t=7 into our equation for the number of students in grades 6 through 12 in 2007.
We found that when t=7, S=30.3. Since we know that the numbers represented are in hundreds, we can multiply the value of S by 100 to get the total number of secondary school students. Let's do it!
30.3* 100=3030
In the context of the situation, this means that in 2007, there were 3030 students enrolled in grades 6 through 12 in this school system.
