The population of the city in the year 2000 is 78,500.
A function assigns the value of each element of one set to the other specific element of another set.
As it is given that the city’s population, P, is modelled by the function,
P(x)= 78,500( 1.02 )ˣ
where x represents the number of years after the year 2000. Now, as we need to know the population of the city in the year 2000, therefore, the value of x will be 0.
Let's substitute the value of x in the modelled function,
[tex]P(x)=78,500(1.02)^x\\\\P(0)=78,500(1.02)^0\\\\P(0)=78,500(1)\\\\P(0)=78,500[/tex]
Hence, the population of the city in the year 2000 is 78,500.
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