QuestionQuestion 4 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 26800. (a) Find a function that models the population $t$ years after 2000 ( $t=0$ for 2000).
Your answer is $P(t)=$ $\square$ (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) $\square$ Question Help: Video Message instructor

Studdy Solution
Calculate $(1.05)^8$ using a calculator:
$(1.05)^8 \approx 1.477455$
Now, calculate $P(8)$ :
$P(8) = 26800 \cdot 1.477455 \approx 39611.794$
Round to the nearest integer:
$P(8) \approx 39612$
The function that models the population is:
$P(t) = 26800 \cdot (1.05)^t$
The estimated fox population in 2008 is:
$\boxed{39612}$

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