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An evergreen nursery usually sells certain shrub after 6 years of growth and shaping: The growth rate during those 6 years is approximated by dh/dt = 1.2t + 2, where t is the time in years and h is the height in centimeters. The seedlings are 15 centimeters tall when planted (t = 0). (a) Find the height after years h(t) (b) How tall are the shrubs when they are sold? cm

Respuesta :

(a) After t years, the height is 18t² + 3t + 10

(b) The shrubs are847 cm tall when they are sold.

Given growth rate

dh/dt = 1.8t + 3

dh = (18t + 3)dt

Integrating this, we have

h = 18t² + 3t + C

When t = 0, h = 10cm

Then

10 = C

So

(a) h = 18t² + 3t + 10

(b) Because they are sold after every 9 years, then at t = 9

h = 18(9)² + 3(9) + 10

= 810 + 27 + 10

= 847 cm

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