Question

Martina opens a savings account with an initial deposit and makes no other deposits or withdrawals. She earns interest on her initial deposit. The total amount of money in her savings account at the end of each year is represented by the sequence shown.

100, 105, 110.25, ...
Which recursive formula can be used to determine the total amount of money earned in any year based on the amount earned in the previous year?

f(n + 1) = f(n) + 5
f(n + 1) = 5f(n)
f(n + 1) = 1.05f(n)
f(n + 1) = 0.05f(n)

Answer 1

@jim_thompson5910

Answer 2

would i do the plug in process @jim_thompson5910

Answer 3

"f(n + 1) = f(n) + 5" means we add 5 to the nth term to get the next term after the nth term

Answer 4

ok

Answer 5

that works from 100 to 105

but does it work from 105 to 110.25 ?

Answer 6

no @jim_thompson5910

Answer 7

so f(n + 1) = f(n) + 5 isn't the rule

Answer 8

try out f(n + 1) = 5f(n)

Answer 9

@gabylovesu Yes you would do the plugin process. You can already eliminate two of them by looking at the sequence 100, 105, 110.25. In the sequence we see that we have a decimal 110.25 so we know it is not going to be
f(n + 1) = f(n) + 5
f(n + 1) = 5f(n)

because if we input 105, these two formulas will not return a decimal so that tells us it either has to be f(n + 1) = 1.05f(n) or f(n + 1) = 0.05f(n) so I would not plugin anything into the first two.

Now, start with C: f(n + 1) = 1.05f(n) and plugin 100 to see if you get 105 and then plugin 105, to see if you get 110.25 . If you do that is the answer. If you don't it will be D. f(n + 1) = .05f(n)