SOLUTION: An evergreen nursery usually sells a certain shrub after 5 years of growth and shaping. The growth rate during those 5 years is approximated by dh/dt = 1.7t + 2, where t is the tim

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Question 1127305: An evergreen nursery usually sells a certain shrub after 5 years of growth and shaping. The growth rate during those 5 years is approximated by dh/dt = 1.7t + 2, where t is the time in years and h is the height in centimeters. The seedlings are 11 centimeters tall when planted (t = 0).
(a) Find the height after t years.
(b) How tall are the shrubs when they are sold?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Integrate dh/dt
+h%28t%29+=+%281.7%2F2%29%2At%5E2+%2B+2t+%2B+c+
+h%280%29+=+11+
+11+=+%281.7%2F2%29%2A0%5E2+%2B+2%2A0+%2B+c+
+c+=+11+
------------------
The height after +t+ yrs is:
+h%28t%29+=+.85t%5E2+%2B+2t+%2B+11+
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When the shrubs are sold,
+h%285%29+=+.85%2A5%5E2+%2B+2%2A5+%2B+11+
+h%285%29+=+21.25+%2B+10+%2B+11+
+h%285%29+=+42.25+ cm