Question 444864: Some types of worms have a remarkable ability to live without m
ID: 3105541 • Letter: Q
Question
Question 444864: Some types of worms have a remarkable ability to live without moisture. The following table from one study shows the number of worms surviving after x days without moisture.x is days and w is worms.
x = 0, 20, 40, 80, 120, 160
w = 50, 48, 45, 36, 20, 3
A) Use the equation W = -0.0014x^2 - 0.076x + 50 to find W for each x-value in the table. (Your can show me one and I may be able to get the rest)
B) Discuss how well this equation approximates the data.
C) Use the equation to estimate the number of worms on day 60 and 180. Which answer is most accurate and explain?
Explanation / Answer
(a) Use the equation W = -0.0014x^2 – 0.076x + 50 to find W for each x-value in the table.
at x = 0 W = -0.0014*0^2 -0.076*0 + 50 = 50
at x= 20 W = -0.0014*20^2 -0.076*20 + 50 = 47.92
at x = 40 W = -0.0014*40^2 -0.076*40 + 50 = 44.72
at x = 80 W = -0.0014*80^2 -0.076*80 + 50 = 34.96
at x = 120 W = -0.0014*120^2 -0.076*120 + 50 = 20.72
at x = 160 W = -0.0014*160^2 -0.076*160 + 50 = 2
b) this equation approx miate the data
because error at x = 0 error 50-50 = 0
error at x = 20 error 48-47.92 = 0.08
error at x = 40 error 45-44.72 = 0.28
error at x = 80 error 36-34.96 = 1.04
error at x = 120 error 20-20.72 = -0.72
error at x = 160 error 3-2 = 1
since all errors in bounded limits we can ssay this equation is well approximated.
c) at x= 60 W = -0.0014*60^2 -0.076*60 + 50 = 40.4
at x = 180 W = -0.0014*180^2 -0.076*180 + 50 = -9.04
at x = 60 is most accurate becuase it is given a valid value (which is between 48 and 44)
while at x = 180 is negative values (how biology worms will be negative?)
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