Blog 2
1. In this application, I’m seeking to measure the height of
ferns over a growing period of five weeks. The question I am posing is “how
tall will a fern get after a five week growing period?” Each week will have a
different rate of change, and will be measured by the equation: Y=x2+x
2. Y=x2+x
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Time (weeks)
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1
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2
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3
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4
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5
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Height (cm)
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2.5
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5
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10
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20
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40
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***Graph Attached
3. By drawing the secant lines from point “two” to points
“three, four, and five” I notice the change of slope per week. From point two’s
connection to point five, the change in slope is enormous, more than doubling
from a slope of “five” to a slope of “ten”, which means that ferns grow tall
relatively quickly: from 5cm to 40cm in five weeks. The other two merely hint
at its progress to this point. Point two’s connection to point four has an
increase of slope from five to seven point five. And from two to three weeks,
the slope is the initial increase of slope: a slope of five.
4. The way I got my
value in part g is by calculating the derivative of the derivative for Y=x2+x
and plugged 5 in for the “a value.” I
derived this derivative from a previous problem that required me to find the
tangent line for a point of my choosing, which, in this case was point two. I
found the slope of the tangent line for point five to detail the difference in
growth rates from point two to point five. The slopes of the tangent lines were
very close to prospective secant lines. Though they were not exact, they were off
by no more than one unit. The work can be found in the document attached.
GS
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hey, gershom,
ReplyDeletethis is a fun topic that you chose! ferns do grow quite quickly!
your table and graphs look good and are pretty easy to read, but in the beginning, your initial question probably should have been at what rate is a fern growing at a particular point in time since we are discussing the IRC which is a rate. also, your units should be cm per week. when you get to the tangent line part, i didn't see the actual calculation of the points that you used to get your value. you only showed the use of the definition of the derivative.
you did a really nice job of calculating the secant line values, though! that seemed to be a hard part of this assignment for most, but you did well on that part. =]
professor little
unfortunately, you also lost points for the post being 2 days late, as well. =/
ReplyDeleteprofessor little