Growth rate of bamboo Bamboo belongs to the grass family and i...

Question

Growth rate of bamboo Bamboo belongs to the grass family and is one of the fastest growing plants in the world.

a. A bamboo shoot was 500 cm tall at 10:00 A.M. and 515 cm tall at 3:00 P.M. Compute the average growth rate of the bamboo shoot in cm/hr over the period of time from 10:00 A.M. to 3:00 P.M.

Accepted Answer

Below there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. In a controlled greenhouse experiment, a genetically modified tomato plant was observed to grow rapidly under optimized conditions. The tomato plant was 60 centimeters tall at 7 a.m. And grew to 78 centimeters by 1 p.m., determined the average growth rate of the tomato plant in centimeters per hour from 7 a.m. to 10 p.m. Awesome. So it appears for this particular problem, we're ultimately trying to figure out the average growth rate of this tomato in units of centimeters per hour from the time interval 7:00 a.m. to 1 p.m. So now that we know that we're all Ultimately trying to figure out the average growth rate of this particular tomato plant, let's read off our multiple choice answers to see what our final answer might be, noting once again that all of our multiple choice answers are in the same units of centimeters per hour. So A is 6, B is 5, C is 4, and D is 3. Awesome. So first off, let us write down all of our known variables. So we're told the initial height of the tomato plant, which we'll call HI, and the initial height HI is going to be equal to 60 centimeters. We're also told the final height of the tomato plant, which we'll call HF, and the final height is equal to 78 centimeters. And we're also told the initial time, which we'll call TI, and the initial time is equal to 7 a.m. And our final time, we're also told, which we'll call TF, and our final time, TF is going to be equal to 1 p.m. Fantastic. So, we also need to note and recall that the time interval, which is delta T, the change in time is equal to TF minus TI. And we also need to recall and note the equation for the average growth rate, which we'll call R, and the average growth rate R will be HF minus HI all divided by delta T. So now, our next step is we need to calculate the time interval from 7:00 a.m. to 10 p.m. and we need to note that from 7 a.m. to 10 p.m. it will be 6 hours. So that will mean that Delta T will be equal to 6 hours. So now, we need to substitute in all of our known variables into our equation to help us solve for the average growth rate. So that will mean that R is equal to, which I did little polls, but you could say that R is equal to. So R is equal to 78 centimeters, so we need to take 78 centimeters because that's our value for HF and we need to subtract our HI value which is 60 centimeters. Divided by 6 hours. And we need to simplify our equation to find the average growth rate. So when we do that, we will find that it's equal to 18 centimeters. Per 6. Hours, which will simplify to simply, R is equal to 3 centimeters per hour. And that's it. That is our final answer. Hooray, we did it. So the average growth rate of this particular tomato plant is 3 centimeters per hour. And this corresponds with multiple choice answer letter D, which once again is 3 centimeters per hour. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Average Rate of Change

Units of Measurement

Time Interval

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