The census bureau for a large country has reported that the

The census bureau for a large country has reported that the country is becoming more diverse. The projected population (in millions) of a certain minority is modeled by the exponential function h left parenthesis t right parenthesis equals 37.98 left parenthesis 1.027 right parenthesis Superscript th(t)=37.98(1.027)t where t=0 corresponds to 2000 and 0 t 50. Complete parts a and b below.

a. Estimate in what year the minority\'s population will double the 2005 population of 43.39million. The minority\'s population will double the 2005 population in ___

Solution

h(t) = 37.98(1.027)^t ; where t=0 corresponds to 2000 and 0 t 50.

in what year the minority\'s population will double the 2005 population of 43.39million?

43.39*2 = 37.98(1.027)^t

2.2848 = 1.027^t

Take log on both sides:

ln(2.2848) = t*ln(1.027)

t = 31.01

It means in year = 2032 population will double the 2005 population of 43.39million