There are currently 4000 birds of a particular species in a national park and their number is increasing at a rate of R(t) = 525e0.05t birds/year. If the proportion of birds that survive t years is given by S(t) = e−0.1t, what do you predict the bird population will be 10 years from now? (Round your answer to the nearest whole number.)

It will be 1790.

Step-by-step explanation:

There are 4000 birds of a particular species in a national park.

Now, the number of birds increasing by the relation birds per year.

So, after 10 years the bird population will become, plus 4000.

That means the population after 10 years will become (865.58 + 4000) = 4865.58.

Now, the proportion of birds that survive t years is given by .

So, after 10 years the proportion of birds that survive after 10 years will be

.

Therefore, the predicted population of birds after 10 years from now will be = 4865.58 × 0.368 = 1790. (Answer)

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