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Today, the population of Canyon Falls is 22,500 and the population of Swift Creek is 15,200. The population of Canyon Falls is decreasing at the rate of 740 people each year while the population of Swift Creek is increasing at the rate of 1,500 people each year. Assuming these rates continue into the future, in how many years from today will the population of Swift Creek equal twice the population of Canyon Falls?

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sqdancefan

Answer:

  10 years

Step-by-step explanation:

Let c and s represent the populations of Canyon Falls and Swift Creek, respectively. For time t in years, the respective populations are ...

  c = 22500 -740t

  s = 15200 +1500t

We want to find t when s = 2c.

  s = 2c

  15200 +1500t = 2(22500 -740t)

  2980t = 29800 . . . . . add 1480-15200, simplify

  29800/2980 = t = 10 . . . . divide by the coefficient of t

The population of Swift Creek will be double that of Canyon Falls in 10 years.

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