e is a special number, so you would need to use a calculator to solve this.
a) replace t in the equation with 5 ( 2005 - 2000 = 5 years)
A = 16.6e^0.0457*5 = 20.86 million Round to nearest tenth = 20.9 million.
b) replace A with 23.3 and solve for t:
23.3 = 16.6e^0.0457*t
Divide both sides by 16.6:
1.4036 = e^0.0457t
Take the natural logarithm of both sides:
0.0457t = LN(1.4036)
Divide both sides by 0.457:
t = LN(1.4036)/0.0457
t = 7.419 years, rounded to nearest tenth = 7.4 years.