Answer:
(1) Let, P represents the size of the bacteria culture in t hours,
According to the question,



By integrating,



Where
,
We have,
at t = 0, P = 200,

at t = 6, P = 1200

Hence, the required function would be,

(2) if t = 7,
The population would be,

(3) If P = 1750,

Hence, it will take about 8 years for the population to reach 1750.