Question

An evergreen nursery usually sells a certain shrub after 7 years of growth and shaping. The growth rate during those 7 years is approximated by dh/dt = 1.2t + 3, 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.

Answer 1

( 0.6 t^2 + 3t + 11 ) cm

Explanation:

dh/dt = 1.2t + 3

at t = 0, h = 11 cm

(a)

dh / dt = 1.2 t + 3

dh = (1.2 t + 3) dt

integrate on both sides

h = 0.6 t^2 + 3t + c .... (1)

where c is the integrating constant

put t = 0

11 = c

Put in equation (1) , we get

h = ( 0.6 t^2 + 3t + 11 ) cm

Thus, teh height of tree after t years is given by

( 0.6 t^2 + 3t + 11 ) cm.