Question

The rate of residential electricity consumption​ (in billions of kilowatt hours​ (kWh) per​ year) of a country is approximated by the model​ below, where x=0 corresponds to the year 1990. Find the total consumption of electricity from 2001 to 2006.

Answer 1

Congrats on making it to integrals!
Basically you need to integral your function because integral rate in respect to time = total amount.
Also your bounts are (2001-1990,2006-1990)=(11,16)

Thus we take integral like:
int(11,16)(928.5e^(0.0249x))=
(11,16)928/0.0249e^(0.0249(x))-928/0.0249e^(0.0249(x))
(You can check this by taking its derivative and seeing if you get the original function)
928/0.0249e^(0.0249(16))-928/0.0249e^(0.0249(11))=6498.1