Question

the table models the balance of a bank account a(t), in dollars, for a given number of days, t.

t	0	1	2	3	4	5
a(t)	450	300	150	0	-150	-300

determine and interpret the x-intercept.
the x-intercept is given by the ordered pair (0, 3). this means that on day 3, the bank account has a balance of $0.
the x-intercept is given by the ordered pair (3, 0). this means that on day 3, the bank account has a balance of $0.
the x-intercept is given by the ordered pair (0, 450). this means that on day 0, the bank account has a balance of $450.
the x-intercept is given by the ordered pair (450, 0). this means that on day 0, the bank account has a balance of $450

Explanation:

The x - intercept of a function \(y = f(x)\) is the point \((x,0)\) where the graph of the function crosses the x - axis. In the context of the function \(A(t)\) (where \(t\) is the independent variable and \(A(t)\) is the dependent variable), we are looking for the value of \(t\) when \(A(t)=0\).

From the table, when \(A(t) = 0\), \(t = 3\). The ordered pair for an x - intercept is \((t,A(t))=(3,0)\) since the x - axis is where \(y = 0\) (in the general \(y=f(x)\) case, here \(y = A(t)\) and \(x=t\)). The interpretation is based on the variables of the problem: \(t\) represents the number of days and \(A(t)\) represents the bank account balance.

Answer:

The x - intercept is given by the ordered pair \((3,0)\). This means that on day 3, the bank account has a balance of \(\$0\).