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The population of a town is decreasing at a rate of 1% per year. In 2000 there were 1300 people. Write an exponential decay function to find the population in 2008. (Round to the nearest whole number).

a) P(t) = 1300(1 - 0.01)ᵗ; P(8) = 1225
b) P(t) = 1300(1 + 0.01)ᵗ; P(8) = 1225
c) P(t) = 1300(1 - 0.01)ᵗ; P(8) = 1181
d) P(t) = 1300(1 + 0.01)ᵗ; P(8) = 1181

User Slavko
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Final answer:

The correct exponential decay function for a town with a population decrease of 1% per year, starting at 1300 people in 2000, is P(t) = 1300(1 - 0.01)^t. To find the population in 2008, we calculate P(8), which results in a rounded population of 1181.

Step-by-step explanation:

To write an exponential decay function for the decreasing population of a town, we start with the initial population and apply the decay rate expressed as a decimal. Since the decay rate is 1% per year, we write it as 0.01. The general form of the exponential decay function is P(t) = P0 * (1 - r)t, where P0 is the initial population, r is the decay rate, and t is time in years.

For the population of 1300 in the year 2000, and a decay rate of 1% per year, the function becomes P(t) = 1300 * (1 - 0.01)t. To find the population in 2008, we substitute 8 for t because 2008 is 8 years after 2000.

Calculating P(8), we have P(8) = 1300 * (1 - 0.01)8. When this is computed, we round to the nearest whole number, resulting in P(8) = 1181. Therefore, the correct exponential decay function and population for the year 2008 is given by option c: P(t) = 1300(1 - 0.01)t; P(8) = 1181.

User Fawzib
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