Respuesta :
Answer:
recursive formula represents the total amount of money in the bank is given by [tex]a_{n+1}=a_n(1.02)^n+15[/tex]
Step-by-step explanation:
Given : Victoria had $200 in her account at the end of one year. At the first of each subsequent year she deposits $15 into the account and earns 2% interest on the new balance.
We have to write a recursive formula representing the total amount of money in the bank.
Since, she has $200 in her account so first term is 200
[tex]a_0=200[/tex]
and At the first of each subsequent year she deposits $15 into the account and earns 2% interest on the new balance.
balance at beginning of year 1 = 200+15=215
[tex]a_1=215[/tex]
at the beginning of year 1 she has balance = 215 + interest on 215 + 15
[tex](1+\frac{r}{100})^n[/tex] , where n is time period.
r = 2%
[tex](1+\frac{2}{100})^n=(1.02)^n[/tex]
Thus, at the beginning of year 1 she has balance =[tex]a_2=215(1.02)+15[/tex]
So at every next year she will have interest on previous balance + $15
So , recursive formula represents the total amount of money in the bank is given by [tex]a_{n+1}=a_n(1.02)^n+15[/tex]
