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University of Houston

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Problem 55

Tree Growth An evergreen nursery usually sells a certain type of shrub after 6 years of growth and shaping. The growth rate during those 6 years is approximated by $d h / d t=1.5 t+5,$ 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 after $t$ years.

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

Answer

$$

69 \mathrm{cm}

$$

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## Discussion

## Video Transcript

all right into by we have the HDP equals one quick five times T plus five. Where are height is centimeter and we have zero. Mama So a You're asking us the height after p years So I want to find my position function So I'm gonna take the integral Oh my each The tea We're equal. The indie grow 1.5 teeth. That's five D. So that's equal. 1.5 is three over two. He square times 1/2 will not play the coefficient baby in verse plus five Teen See And now gonna find my c by using my 0.0 12 when he is zero h is our ancient peas. Flow equals three boards T's were crossed by plus C Bobby, in my 12 year, my zero 34 zero squared plus five times zero we'll see c equals 12 and my position function becomes mooch. Oh, tea equals 34 He's weird plus five t but strong But they were asking for in part a and art be at six years So we're gonna substitute in six Where Billy C A. T. So each six. You won't 34 huh? Waving it three or I'm Thanks. Where? Last five times. Six last. Well, 36 times. 34 27. Tony 7 30 plus gives us, you know, centimeters. And that's part B. Oh, that's it. You're gonna be okay.

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