In a country the windpower capacity has grown exponentially

In a country, the wind-power capacity has grown exponentially from 4726 megawatts in 2002 to 46, 900 megawatts in 2012. a) Find the exponential growth rate k and write an equation for an exponential function that can be used to predict the wind-power capacity, in megawatts t years after 2002. b) Estimate the year in which wind-power capacity will reach 120,000 megawatts. a) The exponential growth rate k is. (Type an integer or decimal rounded to three decimal places as needed.) Using the growth rate k in the previous step, find the equation for an exponential function. P(t) = b) In the year the wind-power capacity will reach 120,000 megawatts. (Round up to the nearest whole number)

Solution

4726 MW in year 2002

46900 MW in year 2012

So, E = Eoe^kt

Eo = 4726

E = 4726e^kt

Now t = 10 yrs , E =46900

46900 = 4726e^k*10

9.9238 = e^10k ; ln(9.9238) = 10k

k = 0.229 ;

In which year E = 120,000

120,000 = 4726e^0.229t

t = 14.124 yr

So, Year = 2002 + 14.124 = 2017 year