Final answer:
The β-1 adrenergic receptor is responsible for increasing the heart rate and force of contraction, as well as elevating metabolic activity under sympathetic nervous system activation.
Step-by-step explanation:
The sympathetic nervous system stimulates certain responses in the body, often related to the fight-or-flight mechanism. Regarding the sympathetic receptors responsible for increasing the heart rate and force of contraction, along with a rise in metabolic activity, the suitable receptor type is the β-1 adrenergic receptor. The β-1 receptors are part of the β-adrenergic group, which interact with epinephrine and norepinephrine, leading to enhanced cardiac output by increasing the heart rate and the force with which the heart ejects blood during each beat (ejection fraction). This is in contrast with the α-2 receptors, which are generally involved with inhibiting norepinephrine release and reducing sympathetic activity.
Hence, in the context of sympathetic activation that increases both heart activity and metabolic rates, β-1 adrenergic receptors play a central role.