Question

A country is not building many nuclear plants, but the ones it has are running at nearly full capacity. The output (as a percent of total capacity) of nuclear plants isdescribed by the equationy-1.92631+ 70.081where t is measured in years, with 1 = corresponding to the beginning of 1990.If the utilization of nuclear power continues to grow at the same rate and the total capacity of nuclear plants in the country remains constant, by what year can theplants be expected to be generating at maximum capacity?

Answer 1

Weare asked to find the year at which a nuclear plant will be working at 100% capacity, given that the expression for the percent of capacity as a function of time is:

y(t) = 1.9263 t + 70.061

Then , we want to find the time "t" when this function will render 100:

100 = 1.9263 t + 70.061

solve for t by subtracting 70.061 from both sides:

100 - 70.061 = 1.9263 t

and then divide both sides by 1.9263:

29.939 / 1.9263 = t

t = 15.5422 years

Notice that this is the number of years counting from 1990 (which is the zero starting point) then we expect the plant to be working at 100 by the year:

1990 + 15.5 = 2005.5, so for sure by 2006 the plant will be working full capacity