The natural resources of an island limit the growth of the population. The population of the island is given by the logistic equation \( \mathrm{P}(\mathrm{t})=\frac{3947}{1+3.69 e^{-0.41 t}} \), where t is the number of years after 1980 . What is the limiting value of the population?

\( \operatorname { tion } ( 6 s - 6 ) ^ { 2 } = 81 \)

\( ( y + x ) d y = ( y - x ) d x \)

Factor the binomial completely. \[ 25 p^{3} q-81 p q^{3} \]

The fox population in a certain region has an annual growth rate of 5 percent per year. It is estimated that the population in the year 2000 was 6300. (a) Find a function that models the population \( t \) years after 2000 ( \( t=0 \) for 2000). Your answer is \( P(t)= \) (b) Use the function from part (a) to estimate the fox population in the year 2008 . Your answer is (the answer should be an integer)

Fill in the blanks of the table that shows logarithmic growth base 6 . -