Question

Nathan has 80 stamps in his collection. He adds 1 stamp to it today. Each day he plans to add twice the number of stamps as the previous day. If he keeps adding stamps at this rate for n days, which recursive function represents the number of stamps he has on any day in the future?

Answer 1

By day 10 he's adding 1,000 stamps per day. By day 20, a million per day. Day 30, a billion stamps per day. Good luck Nathan.

Answer 2

On first day he adds 1 tulip. On second he adds 2 tulips. So on nth day he add 2^(n-1) tulips. As a result, a geometric progression can be set up to know how much he will add on each day
\[\large\rm u_{n}=2^{n-1} \]
Now since we know he already have 80 tulips at start, we can modify the function so we have 80 added already.
\[\large\rm u_{n}=80+2^{n-1} \]

Answer 3

@FaiqRaees he isn't gonna have time for tulips with all that stamp collecting he's gonna be doing.

And the Earth would run out of tulips in a month or two.

Answer 4

@agent0smith Oh yep mistake.
On first day he adds 1stamp. On second he adds 2 stamps. So on nth day he add 2^(n-1) stamps. As a result, a geometric progression can be set up to know how much he will add on each day
\[\large\rm u_{n}=2^{n-1}\]
Now since we know he already have 80 stamps at start, we can modify the function so we have 80 added already.
\[\large\rm u_{n}=80+2^{n-1}\]