Question

The population of Tucson, AZ has been rising according to the model A=p*e^0.036t, where p is the population in 1990 and A is the population t years later. If Tuscon's population was 468,000 in 1990, when is the city expected to reach 1 million people?
a. 1998
b. 2011
c. 1993
d. 1948
e. none

Answer 1

\[1000000 = 468000*e^{0.036t}\]\[1000000/468000=e^{0.036t}\]\[2.136752137 = e^{0.036t}\]\[\ln(2.136752137) = 0.036t\]\[0.7592869832/.036 = t\]=~21 years

1990 + 21 = 2011