Sam opened a savings account with an initial deposit of $2,000. since then, he has never made any other deposits or withdrawals. his savings account earns 0.4% interest monthly and an annual bonus of 1.5% interest. which equation gives the approximate amount, a(x), he has in his savings account as a function of x, the number of years since his initial deposit? a(x) ≈ 2,000 + (1.059)x3 a(x) ≈ 2,000(1.019)x2 a(x) ≈ 2,000(1.065)x a(x) ≈ 2,000(1.059)x2

Third option:

Step-by-step explanation:

Notice if we invest 2,000 then the first month then after the first 0.4% interest is earned we will have in the account:

2,000(1+0.004) = 2,000(1.004)

I just applied the simple interest formula.

Then after the second month we will have:

And so on each month.

So at the end of the first year (12 months) we have:

But we also earn an additional 1.5% in the year, so we will have:

At the end of the second year we will have:

At the end of the third year:

And so on,

So if the number of years is denoted with x, at the end of x years we will have the following amount in the savings:

We use our calculator to simplify that inside the brackets:

Rounding  to the third decimal place we get: 1.065

So notice the amount in the savings after x years will be:

Since they want it in function notation we just write the A(x) that denotes the amount in the savings: