Why does a baby and an adult have different heart beat rates?

Proportional to size. Heart rates are proportional to the size of the human and in fact in all mammals the rate is generally proportional to size with just a few exceptions. Therefore a child will have a faster basic rate than an adult on average if they are otherwise normal.
Metabolism/need. Consider the difference in the two.The baby is a construction zone with a lot of growth and development going on. The adult has finished construction and gone into upkeep mode. Both have the capacity to increase the rate as needed but the baseline is different to meet the different needs of the project at hand.

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