   Chapter 5.2, Problem 57E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Gardening An evergreen nursery usually sells a type of shrub after 5 years of growth and shaping. The growth rate during those 5 years is approximated by d h d t  =  17.6 t 17.6 t 2   +   1 where t is the time (in years) and h is the height (in inches). The seedlings are 6 inches tall when planted ( t =   0 ) .(a) Find the height function.(b) How tall are the shrubs when they are sold?

(a)

To determine

To calculate: The height function h for the growth rate during 5 years approximated by the

equation dhdt=17.6t17.6t2+1 and when t=0, the seedling is 6 in tall.

Explanation

Given Information:

The growth rate during 5 years is approximated by the equation dhdt=17.6t17.6t2+1 and when

t=0, h=6.

Formula Used:

According to the general power rule for integration,

If u is a differentiable function of x, then

undu=un+1n+1+C,

Where n1

Calculation:

Consider the equation dhdt=17.6t17.6t2+1.

Integrate dhdx to obtain h.

h=17.6t17.6t2+1dt

h=122(17.6)t17.6t2+1dt …… (1)

Let 17.6t2+1=u.

Differentiate with respect to t,

ddt(17.6t2+1)=dudtddt(17.6t2)+ddt(1)=dudt2(17.6)t=dudt2(17.6)tdt=du

Substitute the value of 2(17.6)tdt=du and 17

(b)

To determine

To calculate: The height of the shrubs from the height function of part (a) when they are sold.

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