please calculate me number 1, 2, 3, 4, 5, 6, 7. Please write clearly for me. Thanks.

4 Safari (SE @AAQLJ 16 Sat 17 next Mon Forum Grapher Calculus II: 17 Introduction to Differential Equations All lessons due next Monday, 11:00pm - in 3 days Remember that learning is about search, discovery, and your own interpretation of x the ndings. This lesson offers an opportunity to start a forum thread on a topic in sciences where exponential growth, decay, carbon dating played a key role. If you found something on the internet that surprised you and it was related to this lesson, please share with us - this would be an example of participation in our learning endeavor. - Dismiss Live Notes EiExpand A11 PDF-beta . 1 Examples of differential equations - An equation that contains the 2 Slope elds - Differential equations, such as the ones illustrated in the previous 3 Growth and decay equation - A linear rst differential equation given by t'(t) = k*f(t), or by dy/dt = k y by letting y = t'(t) is called the exponential growth and deem 4 Guessing a solution - Let dy/dt = 05 y This means that at any value t the derivative of some function y = f(t) is one halfot'thc function itself, Graphically, 5 The general solution of dy/dy=ky. - All differentiable functions whose instantaneous rates ofchange are proportional to their values must exponential functions. 9:194 4 Safari (SE @AAQEI III. ? E]. 20f5 This is proved... - Population Growth model - The equation dy/dt = k y often models a population growth when multiplying is not offset by limited resources such as space, nutrition or na... 7 Carbon Dating - How to estimate the age of organic remains from archaeological sites - The radioactive decay of carbonA(14)C follows the exponential decay equation: dy/dt = k y, where y is the number ofA(14)C atoms at time t an... . Newton's Law of Cooling - Assume that are are in a room with a constant temperature A = 21"(circ). You leave a hot cup of tea on the table. The initial temperature of... 9 Interest compounded continuously - ...illustration... Let P(t) be the value of an account at time t . The rate of change of P(t) divided by the value P(t) is called the relati... . Interest compounded several times - The term compound interest refers to adding the interest to the principal and then taking the next interest on the principal and the previou... 11 The limit formula for the number e=2.71... - In general if the initial amount P(O) is subjected to an interest of 100 \\%compounded n times a year, the value after one year is P(l) = P(O... . Checking solutions of higher order differential equations - An equation that has the second or higher order derivative of an unknown function is called a higher order differential equation . Physics g... 13 The general solution of the harmonic oscillator equation - The equation m[d"2y]/[dt"2] =-k y is often times called a simple harmonic oscillator equation. A mass m experiences a single force m[d"2y]/[... 9'19 4 a: E) 4 Safari