Ariel deposited $100 into her bank account.each friday she will withdraw 10%of her money in her account to spend.will her bank account be empty after 10 withdraws
+130477 We can model this with the following exponential function:
A = 100(.90)n where A is the value of the account after n withdrawals
So, after 10 witdrawals,we have
A = 100(.90)10 = $34.87 left after 10 withdrawals
This seems counter-intuitive....but we are withdrawing 10% of a smaller and smaller balance as n increases. Theoretically, since an exponential function is never 0, the account is never emptied - there always remains some fraction of one cent, even after infinite withdrawals !!!! (However, the limit of this fuction as n approaches infinity = 0)
+23254 If we do not assume any interest added to her account:
First friday: $100.00 - $10.00 = $90.00
Second friday: $90.00 - $9.00 = $81.00
Third friday: $81.00 - $8.10 = $72.90
Fourth friday: $72.90 - $7.29 = $65.61
etc.
I'll let you finish this; but there will be money left in the account after 10 withdrawals because, even though the account gets smaller, every week a smaller and smaller amount will be withdrawn.
+130477 We can model this with the following exponential function:
A = 100(.90)n where A is the value of the account after n withdrawals
So, after 10 witdrawals,we have
A = 100(.90)10 = $34.87 left after 10 withdrawals
This seems counter-intuitive....but we are withdrawing 10% of a smaller and smaller balance as n increases. Theoretically, since an exponential function is never 0, the account is never emptied - there always remains some fraction of one cent, even after infinite withdrawals !!!! (However, the limit of this fuction as n approaches infinity = 0)
