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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.≤ t ≤

In what year is the population of wolves equal to 80?

Respuesta :

Answer:

The year is 2010.

Step-by-step explanation:

The population of wolves is given by P(t) = 80(0.98)t.

The study has began in the year of 2000 and will end in 2020.

The difference between 2000 and 2009 is 9 years and the difference between 2009 and 2020 is 11 years.

Hence, the maximum value of t is 11.

The domain is [tex]0 \leq t \leq 11[/tex].

The population will be 80, that is P(t) = 80.

Hence, 0.98t = 1, or, t = [tex]\frac{1}{0.98} = \frac{100}{98} = \frac{50}{49}[/tex] ≅1.

In (2009 + 1) = 2010, the population of wolves will be 80.