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 = 1.6t + 3, where t is the time in years and h is the height in centimeters. The seedlings are 13 centimeters tall when planted (t = 0).(a) Find the height after t years.(b) How tall are the shrubs when they are sold?

Answer 1

Answer:  a) height after t years be $h(t)=0.8t^2+3t+13$

b) 73.2 cm

Step-by-step explanation:

Since we have given that

$\dfrac{dh}{dt}=1.6t+3\\\\\int\limits {dh} =\int\limits {1.6t+3} \, dx \\\\h(t)=0.8t^2+3t+C$

Since the seedlings are 13 cm tall.

so, height after t years would be

$h(t)=0.8t^2+3t+13$

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

After 7 years of growth, the height of shrubs would be

$h(7)=0.8(7)^2+3\times 7+13\\\\h(7)=73.2\ cm$

Hence, a) height after t years be $h(t)=0.8t^2+3t+13$

b) 73.2 cm