Answer:
Correct choice is B
Step-by-step explanation:
All three functions are increasing when x is increasing. You can find values of each function when x is "enough large". For example, at x=100,
1. linear function: [tex]y=10\cdot 100=1,000.[/tex]
2. exponential function: [tex]y=5^{100}\approx 0.8\cdot 10^{70}.[/tex]
3. quadratic function: [tex]y=4\cdot 100^2+5\cdot 100=40,500.[/tex]
As you can see, when x approaches positive infinity, the exponential function will exceed both the linear and the quadratic functions.
Also you can use graphical method to get from the attached diagrams result. When x approaches positive infinity, the exponential function will exceed both the linear and the quadratic functions.
Correct choice is B.
