The rate of change of the number of Americans over age 65 with Alzheimer's disease (in millions per year) for the years 2000 through 2050 can be modeled by the differential equation dA/dt = 0.0228A where t is the number of years after 2000
(a) Given that in 2010, Alzheimer's disease affected 5.15 million Americans over age 65, find the particular solution to the differential equation. This solution models the number of Americans over age 65 with Alzheimer's disease.
(b) Use the model found in part (a) to project the number of Americans over age 65 with Alzheimer's disease in 2035.