Question

Mark opened a savings account at his bank with a guaranteed annual interest rate of 5.0% for 5 years. If he deposits $10,000.00 into the account and the interest is compounded annually, the interest on the account is modeled by the function A = 10,000(1 + .05)t.

What is the domain of this function in this context?

Answer 1

The domain of the function is all valid values of t.
Since t cannot be negative, the domain of t is all non-negative numbers, or
0 ≤ t < ∞
In interval notation, t=[0, ∞ )

Answer 2

The domain of this function in this context is:

0 ≤t ≤5 i.e. [0,5]

Explanation:

We are given a function A(t) such that it models the interest on the account which is compounded annually.

The function is given as follows:

`A =10,000(1 + .05)^t.`

We are asked to find the domain of this function.

Domain of a function--

It is the set of all the x-values i.e. the value of the independent variables for which the function is defined.

Here the independent variable is t.

Now, here the interest is to be calculated for 5 years.

This means that the value of t is: 0 ≤t ≤5.