SAT Functions as Models

Correct Answer: D

Solution 1:

Tip: Use a calculator.
We graph $I(t)$ and check its value at $t=1, 2, 3, 4,$ and $5.$ When $t=4$ s, $I(t)=26.2144$ mA, as shown below. Therefore, choice (D) is the correct answer.

Solution 2:

Tip: Plug and check.
Tip: Use a calculator.
We plug each answer choice into the equation and select the one that yields $I(t) \approx 26$ mA.

(A) If $t=1$ s, $I(t)=64\left(\frac{5}{4}\right)^{-1}=51.2$ mA. Wrong.
(B) If $t=2$ s, $I(t)=64\left(\frac{5}{4}\right)^{-2}=41$ mA. Wrong.
(C) If $t=3$ s, $I(t)=64\left(\frac{5}{4}\right)^{-3}=32.8$ mA. Wrong.
(D) If $t=4$ s, $I(t)=64\left(\frac{5}{4}\right)^{-4}=26.2$ mA. This is the correct answer.
(E) If $t=5$ s, $I(t)=64\left(\frac{5}{4}\right)^{-5}=21$ mA. Wrong.

---

---

Incorrect Choices:

(A) , (B) , (C) , and (E)
Solution 1 eliminates these choices geometrically and Solution 2 eliminates them algebraically.