Question

An evergreen nursery usually sells a certain shrub after 6 years of growth and shaping. The growth rate during those 6 years is approximated by dh/dt=3.5t+7 where t is the time in years and h is the height in centimeters. The seedlings are 15 centimeters tall when planted (t=0) . Find the height after t years.

Answer 1

??????? u just need to make a integral there

Answer 2

height (with relation to time) = \[h(t) = 1.75t ^{2} +7t +k\]

Answer 3

and k = starting height of the tree/shrub/bush

Answer 4

so plug in your values for k and t and there's your answer

Answer 5

dh = 3.5t + 7 dt

integrate

h(t) = 7/4 t^2 + 7t + C

15 cm = 7/4 (0)^2 + 7(0) + C

C = 15

\[h(t)+7t^2/4+7t+15\]