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# Solved: Growth Speed The images of trees in Figure P1.68 ISBN: 9780321570567 2

## Solution for problem 64PP Chapter 1

Calculus: Early Transcendentals | 1st Edition

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Problem 64PP

Growth Speed The images of trees in Figure P1.68 come from a catalog advertising fast-growing trees. If we mark the position of the top of the tree in the successive years, as shown in the graph in the figure, we obtain a motion diagram much like ones we have seen for other kinds of motion. The motion isn’t steady, of course. In some months the tree grows rapidly; in other months, quite slowly. We can see, though, that the average speed of growth is fairly constant for the first few years. What is this speed in m/s?

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Step 1 of 3

ANSWER: STEP 1:- Here the growth of the tree is given in units of feets for each year. In the 1 st yr (1 to 2 nd yr) the height of the tree increased by, 21 - 12 = 9 feet. In the 2 nd yr (2 to 3rd yr) the height increased by 30 - 21 =9 feet. The total growth of the tree in the years between 1 to 3 is, 9 +9 = 18 feet. The total time taken for this is 3 - 1 = 2 years So the speed will be, speed = increase in height / time taken---------------------(1) = 18 ft / 2 yrs = 9 ft/yr STEP 2:- But we need to convert...

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Step 3 of 3

##### ISBN: 9780321570567

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