Question

QUESTION 3 In the data below obtained in an experiment dealing with energy utilization, w is the live weight of larvae in grams and r the rate of oxygen consumption in ml/hr. w(grams) 0.020 0.119 0.210 1.32 3.34 5.48 r(ml/hr) 0.180 0.299 0.428 1.15 2.83 4.15 (a) Construct a least-squares function of the form r = bw", where a and b are constants, to approximate the (10) rate of oxygen consumption when the weight is 2 grams. (b) Compute the error associated with the approximation. (5) [15]

Answer 1

I am giving answer of first question that is (a) . not sure about (b). hope the solution will be helpful. Thank you.

solution :- 8 bwa ㅋ ling en coway Inbt en wa 7 enre 7 enr en bt a linw, let enray, enb=aog a = ar logw . 2

y y = aotaire. we have > 0.020 0:119 0.210 1.32 3.34 5.48 8 0.180 0.299 0.428 Liis 2083 4:15. } InW (~)-3.912 -201291-1.561 0.278 11.206 1.701 Inx(9) --- 715 ---20* | -0-8490-1401-0401-423 Now let مرا make table. a sto x2 ny. -3.912 -1.75 15. 304. 6.709. -2.129 -1.207 4.533 2.570 -1.561 -0.849 2.437. 1.325 0:278 o.140 0.077, 0.039 1.206 1.040 1.454. 1:254 1. Fou 1:42 3. 2.893 2.421 E-4.417 - 1:168 26.698 14:318, are [ All values decimal places rounded to 3

in to least Square fit the line y = notaire method normal equations / the are, in na ta, E xi Ź y; -() | =ز i=1 n do Exit a {ni 8 = ² xiyi i=1 i cl ting i=1 n = 6 (we have 6 data Here, points): and وال be comes, o pos 6 ao +(-40417) a -10168, (1183 (4.417) ao + (26.698) ay = 14:318 -Live now solving in and cil we get ao 0.228 al = 0.574 2 now, Inb=ao. ao = b e (0-228) y b e 51.256 an d =0.574,

function of a least square the form X - bwa is 8 (0.574) (1.256) W when weight = Now =2 grams, then 8 = (1.256) x (0.574) +8 = 1.870 ml/hr. will be the consumption onygen approximate