x (days) 0 20 40 80 120 160 W (worms) 50 48 45 36 20 3 Biology Some types of wor

Question

x (days) 0 20 40 80 120 160
W (worms) 50 48 45 36 20 3


Biology Some types of worms have a remarkable ability
to live without moisture. The following table from one
study shows the number of worms W surviving after x
days without moisture.

(a) Use the equation W = -0.0014x^2 – 0.076x + 50 to find W for each x-value in the table.

(b) Discuss how well this equation approximates the
data.

(c) Use this equation to estimate the number of worms on
day 60 and on day 180. Which answer is most accurate?
Explain.

Please show details. Thank you.

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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