Harper deposited $110 into a savings account that earns 3.5% interest a year. The function (R)t models the amount of money Raymond has in his savings account as a function of time (t) in years. R(t)=110(1.025)^t How much more money will Harper have in his savings account than Raymond after two years? A: $2.26 B: $7.83 C: $5.57 D: $3.37

  A.  $2.26

Step-by-step explanation:

An equation for Harper's balance can be written similar to the one written for Raymond's balance. It will be ...

  H(t) = 110(1.035)^t

For t = 2, the two balances will be ...

  H(2) = 110(1.035^2) = 117.83

  R(2) = 110(1.025^2) = 115.57

The difference is ...

  $117.83 -115.57 = $2.26

Harper's account will have $2.26 more.

As a quick estimate or sanity check, you can see that Harper's interest rate is 1% more than Raymond's. So, in 2 years, he will earn a little more than 2% more on his investment than Raymond earns. 2% of $110 is $2.20, so the difference can be expected to be slightly more than this.

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step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for