Question

available in a 12-volt battery, ( v ), is modeled by the equation ( v(t) = 12(0.92)^t ), what is the approximate decrease in voltage between two hours and three hours of the battery running?
81 v
96 v
84 v
66 v

Explanation:

Step1: Find V(2)

Substitute \( t = 2 \) into \( V(t)=12(0.92)^t \).
\( V(2)=12(0.92)^2 = 12\times0.8464 = 10.1568 \)

Step2: Find V(3)

Substitute \( t = 3 \) into \( V(t)=12(0.92)^t \).
\( V(3)=12(0.92)^3 = 12\times0.778688 = 9.344256 \)

Step3: Calculate the decrease

Subtract \( V(3) \) from \( V(2) \):
\( 10.1568 - 9.344256 = 0.812544 \approx 0.81 \) (matching one of the options, likely a typo in the problem's option labels, but the calculation shows ~0.81 V decrease).

Answer:

The approximate decrease in voltage is 0.81 V (assuming the first option is "0.81 V" as per the visible text).