Lesson 5 Group 1A by Roser Gine https://padlet.com/rgine16/nguvg282xq8jjl5c Investigating rates of change en-us 2021-03-07 16:11:17 UTC 2025-12-18 15:05:51 UTC hello@padlet.com Use this Padlet to show how you solve a differential equation rgine16 https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1278859964
You will complete three steps:
1. Verify the solution for your differential equation
2. Use Calculus to solve your differential equation
3. Apply your work to population problems]]> 2021-03-07 16:12:35 UTC https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1278859964 rgine16 https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1278875350 2021-03-07 16:20:31 UTC https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1278875350 Step 1: Verify rgine16 https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1278877953 2021-03-07 16:21:57 UTC https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1278877953 rgine16 https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1278881455 2021-03-07 16:23:39 UTC https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1278881455 Step 2: Solve rgine16 https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1278883447 Solve your differential equation for y]]> 2021-03-07 16:24:35 UTC https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1278883447 Step 3: Apply rgine16 https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1278885156 Use your differential equation and its solution to solve the wolf population problem]]> 2021-03-07 16:25:15 UTC https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1278885156 rgine16 https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1278887649 2021-03-07 16:26:42 UTC https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1278887649 Solution to first differential equation rgine16 https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1282648644 2021-03-08 15:29:51 UTC https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1282648644 https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1282653853 First, find derivative. 

Since this is a first order differential equation. 

dy/dt= kCe^(kt)

Now plug that into differential equation.

kCe^(kt)=k(y-y0)

not the same..., so plug in the other value we know! (y)

kCe^(kt)=k(y0+Ce^(kt)-y0)

kCe^(kt)=kCe^(kt)

This is a solution to the differential equation because RHS=LHS]]> 2021-03-08 15:30:43 UTC https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1282653853 https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1282702212 1)  dy/dt = k(y-y0)

2)  1/(y-y0) dy/dt = k

3)  {1/(y-y0) dy/dt * dt = {k dt

4) {1/(y-y0) dy = {k dt

5) ln |y-y0| = kt + C

6) e^(ln|y-y0|) = e^(kt + C)

7) y-y0 = e^kt * e^C

8) y = e^kt * e^C + y0

9) y = Ce^kt + y0

]]> 2021-03-08 15:38:26 UTC https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1282702212 https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1282729623 2021-03-08 15:42:47 UTC https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1282729623 Additional problem! rgine16 https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1295560816 2021-03-10 23:32:41 UTC https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1295560816 https://padlet.com/rgine16/nguvg282xq8jjl5c/wish/1320895872 a.)
dp/dt=K(1500-w(t))

b.) 
-ln|1500-w|=kt +c
1500-w=e^-kt xe^-c
-w=Ce^-kt-1500
w(t)=Ce^(-kt)+1500

w(0)=500
500=Ce^(-k0)+1500
-1000=C

c.)
w(4)=800
800=-1000e^(-k4)+1500
-700=-1000e^(-k4)
.7=e^(-k4)
ln|.7|=-4k
k=-0.08916874

w(t)=-1000e^(0.08916874t)+1500

d.) 


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