Aboard an orbital research station, Emek and Tara monitored a satellite passing through a region that weakened its signal at regular intervals. Every 4 minutes, the system recorded the signal strength. The first four readings were 96, 72, 54, and 40.5 units. Tara noticed that each reading was 0.75 times the previous one, so the values formed a geometric sequence rather than an arithmetic sequence. Emek represented the pattern with a_n = 96(0.75)^(n - 1), where n was the reading number. The station needed to schedule a transmission at the sixth reading, so they used the rule to calculate a_6 = 96(0.75)^5 = 22.78125 units. They also determined that the sixth reading would occur 20 minutes after the first reading because five 4-minute intervals would have passed. Using both the sequence value and the timing pattern, Emek and Tara programmed the station to transmit at the correct moment, and the satellite received the message successfully.