# 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.
You might need: Calculator

### Problem

Two tanker trucks are being filled with goat's milk at different rates.
The liters of goat's milk in Tanker G after being filled for t minutes is modeled by the exponential function g, left parenthesis, t, right parenthesis, equals, 3, dot, 2, start superscript, t, end superscript.
The liters of goat's milk in Tanker H after being filled for t minutes is modeled by the polynomial function h, left parenthesis, t, right parenthesis, equals, t, left parenthesis, t, plus, 4, right parenthesis, start superscript, 2, end superscript.
The graph below shows the liters of milk in each tank.
Which tanker truck had more goat's milk after 6 minutes?
Please choose from one of the following options.
Which tanker truck had more goat's milk after 9 minutes?
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.