An evergreen nursery usually sells a certain shrub after 5 years of growth and shaping. ?

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 + 3, where t is the time in years and h is the height in centimeters. The seedlings are 18 centimeters tall when planted (t = 0).

(a) Find the height after t years.
h(t) = _

(b) How tall are the shrubs when they are sold?

__ cm

1 Answer
Apr 9, 2018

See below.

Explanation:

We are given:

#(dh)/(dt)=17/10t+3#

This is the derivative of some height function. We need to find this height function, so we integrate.

#int(17/10t+3) dt=17/20t^2+3t+c#

We now need to find the constant of integration #bbc#.

We are told the seedlings are 18cm at #t=0#

Plugging in #t=0# into our integral:

#17/20(0)^2+3(0)+c=18#

#c=18#

a)

So height after t years is:

#color(blue)(17/20t^2+3t+18)#

b)

Height when sold after 5 years:

#17/20t^2+3t+18#

Plug in #t=5#

#17/20(5)^2+3(5)+18=217/4=color(blue)(54.25 \ \ cm)#