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Wireless networks have a constraint on their functional lifetime. This is due to the limited energy capacity of batteries powering the wireless nodes. For extending the lifetime of such battery-operated networks, we present a scheme for dynamically selecting the transmission rate for each node in the network. The transmission rate is based on the available energy budget in each node's battery. The goal is to increase the network capability of delivering more packets. The rate selection for each node is subject to satisfying a QoS timing constraint on the packet delivery time. Through adaptively varying each node's rate, we extended the lifetime 10 times on average more transmitting at a maximum rate and delivered on average 7.5 times more data packets. When compared with a scheme that transmits data at a lower rates independent of the battery levels, our scheme delivers up to 12% more packets for the same available total energy.