Question

The capacities at which U.S. nuclear power plants are working are shown in the table for various years.

Year	Percent
1975	56
1980	59
1985	58
1990	70
1995	76
2000	88
2004	89

Let f(t)f(t) be the capacity (in percent) at which U.S. nuclear power plants are working at t years since 1970. A model of the situation is f(t)=0.027t2+0.216t+53.296f(t)=0.027t2+0.216t+53.296.

Use a graphing calculator to draw the graph of the model and, in the same viewing window, the scattergram of the data. Does the model fit the data well?

• The function is not a good model for the data
• The function is a good model for the data.

Estimate at what capacity U. S. nuclear power plants were working in 2012.

% Round to the nearest whole percent.

Predict when U. S. nuclear power plants will be working at full (100%) capacity.

Enter the year this occurs.

Answer 1

Solution)

The graph is as follows

From the graph it xan be concluded that

The function is a good model for the data.

At 2012 the t= 42,

Percent operation is = 109.996% ≈ 110% ....(answer)

For plant to work at 100% we draw a line at y=100, and the point of intersection gives t

Thus t= 37.783 years

The year when this occurs =1970+t= 2007.783

Thus 100% capacity operation shall occur in the year 2007 ....(answer)