Final answer:
The correct formula for the exponential function based on the given information is C) N(t) = 2 × (1/9)t/2. This formula captures the initial value of 2 and the way the function decreases exponentially by having the base of (1/9) to the power of (t/2).
Step-by-step explanation:
To find a formula for the exponential function N = N(t), given that the initial value of N is 2 and that increasing t by 2 divides N by 9, we need to express this relationship using an exponential equation. Since the initial value of N is 2, this is our starting value, often referred to as N0. The description of how the function changes with time tells us that for every increment of 2 in t, N is multiplied by the reciprocal of 9, which is 1/9.
Therefore, the formula for N as a function of t (N(t)) should involve an exponent that changes with t. To find the right base for the exponential, we note that since increasing t by 2 divides N by 9, an increment of 1 in t should divide N by the square root of 9, which is 3. Thus, our base becomes 1/3, and our formula for N over time is N(t) = N0 × (1/3)t/2, where t/2 indicates that for every increase of 2 in t, the base 1/3 is applied once.
The correct formula, given the options is C) N(t) = 2 × (1/9)t/2, reflecting the initial value of 2 and the decrease by a factor of 1/9 for every 2 units of time that passes. This formula aligns with the characteristics of an exponential decay process.