To find the increase in tuition and the total tuition for the 2009-2010 school year, we can follow these steps:

1. Calculate the Increase in Tuition:

   • Initial tuition in 2001: $4520$
   • Percentage increase: $83.9\%$

   The increase in tuition from 2001 to 2009 is given by: $\text{Increase} = 4520 \times \frac{83.9}{100} = 4520 \times 0.839 = 3796.28$

2. Calculate the Total Tuition in 2009:

   • Total tuition for 2009 is the sum of the initial tuition and the increase: $\text{Tuition in 2009} = 4520 + 3796.28 = 8316.28$

So, the increase in tuition is $3796.28, and the tuition for the 2009-2010 school year is $8316.28.

Would you like more details on this calculation or have any questions?

Here are some related questions for further exploration:

1. How would the calculation change if the percentage increase were different?
2. What would the tuition be if another 10% increase occurred in 2010?
3. How much would tuition have increased if the rate were compounded annually?
4. How does a linear increase compare to a percentage increase over multiple years?
5. How can we estimate future tuition costs based on historical percentage increases?

Tip: Always check if percentage increases are compounded annually or applied over a set period, as it affects the final amount.