Answer:
(a)[tex]h(t)=\frac{1.3t^2}{2} + 2t +17[/tex]
(b)62.85cm
Step-by-step explanation:
The growth rate of the shrub is given as:
[tex]\frac{dh}{dt} = 1.3t + 2[/tex]
Where t=time in years, h=height in centimeters
(a)First, we solve for the height h(t) by integrating.
[tex]\int \frac{dh}{dt} dt= \int (1.3t + 2)dt\\h(t)=\frac{1.3t^2}{2} + 2t +C, $ C a constant of Integration$\\$We sunstitute the initial value to find the value of C$\\$When t=0, h=17cm$\\17=C\\Therefore:\\h(t)=\frac{1.3t^2}{2} + 2t +17[/tex]
(b)The shrub are sold after 7 years of growth. Therefore, we determine the value of h(t) when t=7 years.
[tex]h(t)=\frac{1.3t^2}{2} + 2t +17\\h(7)=\frac{1.3*7^2}{2} + 2(7) +17\\=31.85+14+17\\h(7)=62.85cm[/tex]
The Shrubs are 62.85cm tall when they are sold.
