The prepositions 随着 and 跟着 emphasize that one thing follows another.
随着 and 跟着 are followed either by a noun or a pronoun. They are followed by a verb
Scheme
subject
随着/跟着
object
who?/what?
predicate
Pay attention
In this meaning, the preposition 跟着 is used more often than 随着.
Examples
这些垃圾随着河水流到了这里
The garbage flowed here from the river
zhèxiē lājī suízhe héshuǐliú dào le zhèlǐ
他跟着我们走
He's following us
tā gēnzhe wǒmen zǒu
跟着 can also serve as a verb "to follow".
Examples
请跟着导游
Please follow your tour guide
qǐng gēnzhe dǎoyóu
The other meaning of 随着
The preposition 随着 is also used to indicate that a change in the first part of the sentence causes a change in the second part of the sentence. In this case, it is translated as "accordingly, as".
Examples
随着人口数量的减少,经济的问题越来越多了
The economy is becoming more and more problematic with the decreasing population
suízhe rénkǒu shùliàng de jiǎnshǎo, jīngjì de wèntí yuè lái yuè duō le
性格随着年龄改变了
A person’s character changes with age
xìnggé suízhe niánlíng gǎibiàn le
The other meaning of 随着
The other meaning of 随着 is "in the wake of". It conveys the meaning "do the same as someone else".