Code to begin with:import numpy as npfrom scipy.integrate import solve_ivpimport matplotlib.pyplot as plt Question:3.The police arrive at the home of Robert Durst, the trading network leader, to arrest himfor questioning. However, Robert Durst is found dead in his home, strangled to death. Paramedicsrecord his core body temperature to be 25.0°C at 11:15pm on June 12. Normal body temperature is37.5°C.The forensic technicians also sample the concentration of two blood-borne bacterial populations,labelled A and B. In a living person, these populations are held constant at 1 unit per cubic mil-limetre of blood, denoted 1. But after a person dies, these bacterial populations begin to flour-ish since the body's immune system is no longer functioning. The populations (in units) aregoverned by the differential equationsdA 0.0008(T29)2 (1-e0.08(T-45)) A(30-A) for 29 ≤ T ≤ 45{dt0otherwisedBdt0.001 (T-17)² (1-e0.05(T-32)) B(20 − B) for 17 ≤ T ≤ 320otherwisedT= -0.dtmm3At the time of discovery, the concentration of bacteria A was 6.6, and 11.8 for bacteria B.Note that the active metabolism of these bacterial populations heats the body slightly. Taking thismetabolic heating into consideration, the body's core temperature follows the differential equation-0.1 (T-Ta(t))+A + B100(1)where To is the ambient air temperate (in °C), t is measured in hours, and A and B are the concen-trations of bacteria A and B, respectively (in units of).Alibis for the prime suspects for June 12:• Dennis Reader(2)The ambient temperature in Mr. Durst's home is controlled by an automatic thermostat; it's setto maintain 22°C between the hours of 7:00am and 7:00pm, and maintain 16°C from 7:00pm until7:00am the next morning. It takes 30 minutes for the temperature to increase from 16°C to 22°C inthe morning (ie. from 7:00am until 7:30am), but takes about 2 hours to steadily drop from 22°C to16°C at night (from 7:00pm until 9:00pm). You may assume these temperature changes are linearin time.(a) Add code to the notebook that implements the dynamics function for the system of differentialequations that govern T, A, and B, starting at the time of death. You may create and use helperfunctions.9:00am-11:00am Working in retail store (confirmed)11:00am-12:30pm Lunch in the food court (unconfirmed)12:30pm-4:00pm Working in retail store (confirmed)(3)(b) Use your model to try to estimate the time of death. Add lines to the notebook that start thesimulation at the time you think the death occurred, and run it until 11:15pm to see if you cangenerate the same body/bacterial state. Display the final state (at 11:15pm). Also, create aplot of time versus body temperature, starting with your estimated time of death, and endingat 11:15pm on June 12.(c) Considering the alibis below, who do you think killed Robert Durst?• Samantha Brundi9:00am-11:00am Played squash with friend (confirmed)11:00am-1:00pm Lunch with family (confirmed)1:00pm-3:00pm At home watching TV (unconfirmed)• James Carver9:00am-10:30am Went running (unconfirmed)10:30am-1:00pm Driving to out-of-town meeting (2.5 hour drive)1:00pm-3:00pm Meeting (confirmed)

To implement the dynamics function for the system of differential equations, we first define a…

Answered: Code to begin with: import numpy as np…

Engineering

Computer Science

Code to begin with: import numpy as np from scipy.integrate import solve_ivp import matplotlib.pyplot as plt

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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