Question

The amount​ (in megawatts) of energy generated in a country from wind power can be modeled by the function ​W(t)equalsw0​(1.90​)t​, where tequals0 corresponds to the year 2000. ​(a) The amount generated in the year 2000 was 2540 megawatts. Find w0. ​(b) Estimate the amount of energy generated by wind power in the years 2004 and 2013.

Answer 1

Answer with Step-by-step explanation:

We are given that

$W(t)=W_0(1.90)^t$

Where t corresponds to the year 2000=0

a.$W(0)=2540MW$

Substitute the values

$2540\times 10^6=W_0(1.90)^0=W_0$

$W_0=2540MW$

b.In  2004

t=4

$W(4)=2540(1.90)^4$

$W(4)=33101.534 MW$

c.In 2013

t=13

$W(13)=2540(1.9)^{13}=10.68\times 10^6MW$