Question

xIS le6:Critical Thinking Desm os l Graphing Calculator sassign ments/177236?module Jtem id-439078 -option #1: Working with Radioactive Material a scientist, you study 1000 grams of a radioactive material for several months and you have obtained the following data: Month Weight 0 1000 749.8 12 562.14 18 421.5 24 316 30 236.93 36 177.64 Note that you are asked to use a graphing utility in this assignment Module 6: Critical ThinkingXDesmos Graphing Calculator re.com/courses/9495/assignments/1772362module tem ud-439876 236.93 177.64 Note that you are asked to use a graphing utility in this assignment. Arecommended online utility is https:llwww.desmes.com/calculator .It allows graphing and then copying and posting into a Word document Using a graphing utility, draw a scatter diagram with month and weight as your - variables. Using a graphing utility, build an exponential model from the data. . Express the weight as the function of months . Graph the exponential function in the scatter diagram. . Interpret the constant parameters of this function. Determine the half-life of the radioactive material . . How much radioactive material will be ileft after 30 months? When will you have 40 grams of this radioactive material? . . Requirements:

Answer 1

Mathematica Sun May 26, 12:24 PM Untitled-1.nb*-Wolfram Mathematica 11.3 Eile Eet sert Format Cell graphics Faluatien Palettes Windam Hep This is Mathematica Software Let Q(t) be the amount of radioactive material left at time t. Infil-data= {{6, 1000), {6, 749.8), {12, 562 . 14), {18, 421.5), {24, 316), {39, 236.93), {36, 177 .64)) Out11- ((8, 1009), (6, 749.8), [12, 562.14), (18, 421.5), (24, 316), (38, 236.93), (36, 177.64} } In2- model-aExp-k t] Inl3 fit FindFit[data, model, (a, k), t] P1; ListPlot [data, AxesLabel → {t, "0(t)")) Inf4- ait) 1000 800 600 400 200 10 20 25 30 35

Mathematica Sun May 26, 12:25 PM Untitled-1.nb*-Wolfram Mathematica 11.3 Eile Eet sert Format Cell graphics Faluatien Palettes Windam Hep (5- a-al. fitti 1000.01 u0.6479995 Weight in terms of months is Q(t) = ae-kt, where a =1000 and k = 0.0479995 Inf7-P2-plot [a * Exp [-k * t), {t, θ , 36), PlotStyle → Red] 1000 900 600 400 200 25 35 10 labels. s-Image ibeckground..

Mathematica Sun May 26, 12:25 PM Untitled-1.nb*-Wolfram Mathematica 11.3 Eile Eet sert Format Cell graphics Faluatien Palettes Windam Hep ShowP, P2] an) 1000 B00 600 Ou[B] 100 200 20 25 30 35 label., anes, imag·'", background , more le | * a- amount of radioactive material in grams at time t 0. k rate of decay of radioactive material. Unit of is grams/month Half life of the radioactive material is In(9l- Solve [500aExp-k*t], t] {{t-14.441 } } any Hence half life is 14.441 months. 150%-

Mathematica Sun May 26, 12:25 PM Untitled-1.nb*-Wolfram Mathematica 11.3 Eile Eet sert Format Cell graphics Faluatien Palettes Windam Hep Radioactive material left (in grams) after 30 months is n[10) อา 0410-236 .935 ยู่า Time (in months) when 40 grams of radioactive material is left is In[11]-Solve [40 = a * Exp [-ke t] , t] ut 67.0609 Hence after 67 months 40grams of radioactive substance is left.