5.12.5 Practice

For questions 1 - 5, use the the three exponential functions defined below:

• $f(x)=100\cdot <!--\; \cdot \; -->3^x$
• $g(x)=100\cdot <!--\; \cdot \; -->(3.5{)}^x$
• $h(x)=100\cdot <!--\; \cdot \; -->4^x$

1. Which of these functions grows the least quickly?

2. Which function grows the most quickly?

The three given graphs represent the functions $f$, $g$, and $h$ defined above.

3. Which graph corresponds to $f(x)$?

4. Which graph corresponds to $g(x)$?

5. Which graph corresponds to $h(x)$?

6. Which graph matches the equation $y=20\cdot <!--\; \cdot \; -->3^x$

7. Which graph matches the equation $y=50\cdot <!--\; \cdot \; -->3^x$

8. Which graph matches the equation $y=100\cdot <!--\; \cdot \; -->3^x$

9. Written in the form $f(x)=a\cdot <!--\; \cdot \; -->b^x$, what is the value of $a$ for each function?

10. Which graph decreases the most quickly?

The graphs of $y=50\cdot <!--\; \cdot \; -->2^x$, $y=200\cdot <!--\; \cdot \; -->2^x$, and $y=100\cdot <!--\; \cdot \; -->2^x$ are shown.

11. Which is the graph of $y=100\cdot <!--\; \cdot \; -->2^x$?

12. Which of the functions graphed, $y=a\cdot <!--\; \cdot \; -->b^x$, has the smallest value for $a$?

13. Which of the functions graphed, $y=a\cdot <!--\; \cdot \; -->b^x$, has the lowest value for $b$?

14. What is the equation of the horizontal asymptote for $f(x)=5\cdot <!--\; \cdot \; -->2^x-<!--\; -\; -->3$?