Problem:
The number of geese in a flock increases so that the difference between the populations in year and year is directly proportional to the population in year . If the populations in the years and were and respectively, then the population in was
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Solution:
Let be the number of geese in , and let be the constant of proportionality. Then and . Solve the second equation for , and use that value to solve for in the first equation, obtaining . Thus . Factoring yields . Since is positive, it follows that .