Math
posted by Zach on .
your aunt gives you a check on your birthday each year. on your first birthday , she gives you a check for one cent. the next year she gives you 3 cents , then 9. each year she triples the amount of the previous year 's check. how old will you be when she gives you a check worth more than 1000$ ? how much money will you receive on your 18th birthday?

1c. = 3^0,
3c = 3^1,
9c. = 3^2,
27c = #^3.
So we have base 3 numerals.
A = 3^(n1). A = Amount in cents @ nth year.
a. 3^(n1) = 100,000 cents.
(n1)Log3 = Log100,000,
n1 = Log100,000 / Log3 = 10.5,
n = 11.5 years of age.
b. A = 3^(181),
A = 3^17 = 129,140,163 cents,
A = $1,291,401.63.