Modeling Circuit Charge and Exponential Growth of Toads
School
University of Guelph**We aren't endorsed by this school
Course
MATH 2270
Subject
Mathematics
Date
Dec 12, 2024
Pages
1
Uploaded by ChancellorSeaLion4237
Lab Test 2Math*2270, Fall 2023Week of November 13, 2023Q1. Consider the following circuit diagram:A mad scientist named Dr. Nerbert (“Nerr-Nerr”, according to her final remainingcolleague) is designing a Very Important Machine, whose main circuit somehowhappens to be a simple closed loop. She has a battery that she has designed togradually increase the applied voltage, givingE(t) = 2tvolts (wheretis the time inseconds); the resistance in this circuit isR= 100 Ω, and there is also aC=1500Fcapacitor. Assume that the charge at timet= 0 is zero, whereupon the switch isclosed and the loop is completed.Set up and solve an IVP modelling Nerr-Nerr’s machine, with the dependentvariableq(t) representing the charge on the capacitor at timet.(6 marks)Q2. Suppose 4000 individuals of a species of toad are introduced to a new setting.The toads undergo explosive (exponential) growth. After 6 months, 5000individuals are counted. Assuming the growth remains exponential and the count isaccurate, determine the following:•a) The number of toads expected 2 years after they were introduced.•b) The doubling time for the number of toads.You do not need to set up or solve a DE to answer this problem, but show at leasta little work. (4 marks)
