Final Answer:
The equation to calculate the cost of other colleges next year (n) based on this year's cost (t), with a 3.5% increase, is n = t + 0.035 × t.
Step-by-step explanation:
To calculate the cost of other colleges next year, given this year's cost (t) and an expected 3.5% increase, the equation involves adding the percentage increase to the current cost. Using ( n ) to denote next year's cost and (t) for this year's cost, the equation ( n = t + 0.035 × t ) reflects the 3.5% increment applied to this year's cost.
This equation is derived from the concept of finding the percentage increase. The formula for calculating the increase in percentage involves adding the percentage increase to 100% (the original value). For a 3.5% increase, the equation can be written as ( 100% + 3.5% = 103.5% ), which translates mathematically to ( 1 + 0.035 = 1.035 ). Therefore, to calculate the next year's cost, you multiply this factor (1.035) by the current year's cost (t) and add it to the original cost, resulting in ( n = t + 0.035 × t).
For instance, if this year's cost for a college is $20,000, the calculation for next year's cost (n) would be ( n = 20,000 + 0.035 × 20,000 = 20,000 × 1.035 = 20,700 ). Therefore, the cost for next year would be $20,700 after applying the 3.5% increase to the initial cost of $20,000.
In summary, using the equation ( n = t + 0.035 × t) allows for straightforward calculation of next year's cost for any college, with t representing this year's cost and n representing next year's cost, considering a 3.5% increase.