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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5.1, Problem 70E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Gardening An evergreen nursery usually sells a certain shrub after 6 years of growth and shaping. The growth rate during those 6 years is approximated by dh/dt = 1.5t + 5, 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 function.

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

(a)

To determine

To calculate: The height function of certain shrub whose growth rate is dhdt=1.5t+5, where t is the time (in years) h is the height (in centimeters) for 6 years.

Explanation

Given Information:

The shrub used to sell after 6 years of growth and shaping and the seedlings are 12 centimeters tall when planted. The growth rate of the shrub is dhdt=1.5t+5.

Formula used:

The simple power rule of integration ∫xndx=xn+1n+1+C.

Calculation:

Consider the growth rate of the shrub is dhdt=1.5t+5.

Integrate the provided growth rate, use the simple power rule of integration ∫xndx=xn+1n+1+C.

∫dhdtdt=∫(1.5t+5)dth(t)=1.5∫tdt+5∫dt=1.5[t1+11+1]+5t+C=0

(b)

To determine

To calculate: The height of the shrubs when they are sold.

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