Given:
The enrollment increases by approximately the same percentage between 2000 and 2010 as it decreased between 1950 and 1960.
To find:
The expected enrollment in 2010.
Solution:
Percentage decrease formula:
[tex]\%\text{ decrease}=\dfrac{\text{Initial value - New value}}{\text{Initial value}}\times 100[/tex]
The percentage decrease in between 1950 and 1960 is:
[tex]\%\text{ decrease}=\dfrac{4-3.5}{4}\times 100[/tex]
[tex]\%\text{ decrease}=\dfrac{0.5}{4}\times 100[/tex]
[tex]\%\text{ decrease}=\dfrac{50}{4}[/tex]
[tex]\%\text{ decrease}=12.5[/tex]
The enrollment decreased by 12.5% between 1950 and 1960. So, the enrollment increases by 12.5% between 2000 and 2010.
The expected enrollment in 2010 is:
[tex]\text{Expected enrollment}=7+\dfrac{12.5}{100}\times 7[/tex]
[tex]\text{Expected enrollment}=7+0.875[/tex]
[tex]\text{Expected enrollment}=7.875[/tex]
Therefore, the expected enrollment in 2010 is 7.875 thousands.