SOLUTION: Please help me solve this equation. A herd of deer is introduced onto a small island. At first the herd increases rapidly, but eventually food resources dwindle and the populatio

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Question 845157: Please help me solve this equation.
A herd of deer is introduced onto a small island. At first the herd increases rapidly, but eventually food resources dwindle and the population declines. It can be shown by means of calculus that the rate R (in deer per year) at which the deer population changes at time t is given by R = −4t3 + 26t.
(a) When does the population cease to grow? (Round your answer to two decimal places.)
after t = years
(b) Determine the positive values of t for which R > 0. (Enter your answer using interval notation.)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+R+=+-4t%5E3+%2B+26t+
Here's the plot:
+graph%28+400%2C+400%2C+-5%2C+5%2C+-30%2C+30%2C+-4x%5E3+%2B+26x+%29+
What are the values of +t+ for which +R+=+0+?
+-4t%5E3+%2B+26t+=+0+
+t%2A%28+-4t%5E2+%2B+26+%29+=+0+
+t+=+0+
and
+-4t%5E2+%2B+26+=+0+
+4t%5E2+=+26+
+t%5E2+=+13%2F2+
+t+=+2.55+
The population stops growing ( +R+=+0+ )
when +t+=+2.55+ years
-------------------------
The population growth is positive between
+t+=+0+ and +t+=+2.55+ years
Disregard all the negative time on plot