# data[].attributes.body
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.)

# data[].attributes.body
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

# data[].attributes.body
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

# data[].attributes.body
Use your differential equation and its solution to solve the wolf population problem

# data[].attributes.body
Solve your differential equation for y

# data[].attributes.headline
Use this Padlet to show how you solve a differential equation

# data[].attributes.subject
Use this Padlet to show how you solve a differential equation

# data[].attributes.body
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