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
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
See below.
Explanation:
We are given:
This is the derivative of some height function. We need to find this height function, so we integrate.
We now need to find the constant of integration
We are told the seedlings are 18cm at
Plugging in
a)
So height after t years is:
b)
Height when sold after 5 years:
Plug in