# Compare growth of exponentials & polynomials

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 cultures of bacteria grow at different rates.
The number of bacteria present in Culture X after t hours is modeled by the polynomial function x, left parenthesis, t, right parenthesis, equals, 10, t, start superscript, 2, end superscript.
The number of bacteria present in Culture Y after t hours is modeled by the exponential function y, left parenthesis, t, right parenthesis, equals, 2, start superscript, t, end superscript.
The graph below shows the number of bacteria in each culture.
Which culture had more bacteria after 5 hours ?
Please choose from one of the following options.
Which culture had more bacteria after 10 hours ?
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.