Question

Chegg 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 = 1.5t + 4, where t is the time in years and h is the height in centimeters. The seedlings are 12 centimeters tall when planted (t = 0). (a) Find the height after t years.

Answer 1

Answer:

h(t) = 1.5t²/2 + 4t +12

Step-by-step explanation:

The growth rate is given by

dh/dt = 1.5t + 4

To determine the height of the seedlings we integrate the rate with respect to t.

The integral of dh/dt = integral of 1.5t + integral of 4

The integral of dh/dt = h

The integral of dh/dt = 1.5t²/2 + 4t

So at t = 0

h = 12

That makes the equation

h = 1.5t²/2 + 4t +12

Where 12 is the constant

So h(t) = 1.5t²/2 + 4t +12

Will give us the height after t years