Practice analyzing the end behavior of two functions that model similar real-world relationship, where one function is exponential and the other is polynomial.
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Problem

Two cities are building bicycle paths.
The total kilometers of new bicycle paths built in Charles City after the first t months is modeled by the polynomial function c, left parenthesis, t, right parenthesis, equals, 6, t, start superscript, 2, end superscript, plus, 15, t.
The total kilometers of new bicycle paths built in Tinsel Town after the first t months is modeled by the exponential function n, left parenthesis, t, right parenthesis, equals, 5, dot, 2, start superscript, t, end superscript.
The graph below shows the amount of bicycle paths built by each city.
After 3 months which city had built more new bicycle paths?
Please choose from one of the following options.
After 6 months which city had built more new bicycle paths?
Please choose from one of the following options.
Which function seems to eventually exceed the other and have greater outputs for large t values?
Please choose from one of the following options.