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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.

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Answer with Step-by-step explanation:

We are given that

[tex]W(t)=W_0(1.90)^t[/tex]

Where t corresponds to the year 2000=0

a.[tex]W(0)=2540MW[/tex]

Substitute the values

[tex]2540\times 10^6=W_0(1.90)^0=W_0[/tex]

[tex]W_0=2540MW[/tex]

b.In  2004

t=4

[tex]W(4)=2540(1.90)^4[/tex]

[tex]W(4)=33101.534 MW[/tex]

c.In 2013

t=13

[tex]W(13)=2540(1.9)^{13}=10.68\times 10^6MW[/tex]

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