ANSWER
The population of the rural city in 2035 is approximately 16735
EXPLANATION
The exponential equation that models the population of the rural city is
[tex]P(t)=2600^{0.038t} [/tex]
where t is the number of years after 1986.
To find the approximate population in 2035, we need to calculate the number of years that have passed.
We therefore subtract 1986 from 2035 to get,
2035-1986=49
We put t= 49 to obtain,
[tex]P(49)=2600^{0.038(49)} = 16735.15[/tex]
Hence the population of the rural city in 2035 is approximately 16735
