The value 0.983 in the function f(t) = 7.28(0.983)^t represents the annual decay rate of the town's population over time t.

Mathematics · Middle School · Thu Feb 04 2021

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In the function f(t) = 7,280 * (0.983)^t, which models the population of a town after t years, the value 0.983 is the growth rate factor per year, representing a decreasing population. Specifically, 0.983 is less than 1, which indicates that the population decreases by a certain percentage each year rather than increases.

The growth rate factor is calculated as 1 minus the decay (or reduction) rate in percentage. Since the growth rate factor is 0.983, we can determine the percentage decrease each year by subtracting this value from 1 and then converting the result into a percentage:

1 - 0.983 = 0.017 (which is the decay rate)

0.017 * 100 = 1.7%

So, 0.983 represents that the population of the town is decreasing at an annual rate of 1.7%. Therefore, each year, the population is 98.3% (which is 100% - 1.7%) of what it was the previous year.