A study on the population of wolves is being done in a county to determine how the number of wolves has changed over time. The population of wolves is being modeled by the function P (t) = 80 (0.98) t, where t is the number of years since 2009. What is an appropriate domain for this function if the study will end in the year 2020 and began in year 2000? Fill in the blanks so that the appropriate domain is described.

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Mathematics

Tootsie

27 November, 19:21

A study on the population of wolves is being done in a county to determine how the number of wolves has changed over time. The population of wolves is being modeled by the function P (t) = 80 (0.98) t, where t is the number of years since 2009. What is an appropriate domain for this function if the study will end in the year 2020 and began in year 2000? Fill in the blanks so that the appropriate domain is described.

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Gerardo Hobbs · Answer 1

Domain is the years from 2000 through 2020 inclusive

at 2000, t = 2000-2009 = - 9

at 2020, t = 2020-2009 = 11

Domain: - 9 ≤ t ≤ 11

P (t) = 80 (0.98) t

Since population models are almost always exponential, I'll assume you meant the "t" to be an exponent and the model should be:

P (t) = 80•0.98^t = 80 → t = 0

The population is 80 at t = 0. The year corresponding to t = 0 is 2009