Question

Total power generated by wind worldwide doubles every 3 years. In a particular year, the world wind-generating capacity was about 90 thousand megawatts. Find the continuous growth rate as a percent and give a formula for wind generating capacity W (in thousand megawatts) as a function of t, the number of years in the future.

Answer 1

I'm not sure what I am doing wrong...
So far, I have...
W(t)=ae^kt
W(3)=90e^3k
180=90e^3k
2=e^3k
ln(2)/3 = k
.231 = k
So, 23% ? & that would make my equation W(t)=90e^(.231t)

Answer 2

ok

Answer 3

at what growth rate would it be doubling every 3 years

Answer 4

growth rate per year

Answer 5

x(1+r)^3=2x
so r=2^(1/3) -1

Answer 6

now we know the growth rate per year we are dealing with

Answer 7

dy/dx= r*y

Answer 8

alll that is left is to solve this differential equation

Answer 9

and solve it for our initial condition

Answer 10

@ganeshie8 does this work?

Answer 11

dont worry Ganeishie will check it for us, let me try to sovle completely meanwhile

Answer 12

oh i cant use that 2^(1/3)-1 formula, because this s contrinous!

Answer 13

y=90e^(.231t), is right

Answer 14

dy/dx=ky
dy/y=kdx
ln y= kx + c
y=ce^kx
y(0)=90 setting this gives c=90
y=90*e^kx
y(3)=180=90e*3k
k=ln(2)/3