Let's look at some of the connections between the multiple representations of an exponential function. a. Arnold dropped a ball during the bouncing ball activity and recorded its height in a table. What was the rebound ratio of his ball? At what height did he drop the ball? Write an equation that represents his data. Explain your equation.
Bounce Number Height(cm)
0 84.5 3
1 67.6 4
2 54.1
b. A major technology company, ExpoGrow, is growing incredibly fast. The latest prospectus (a report on the company) said that so far, the number of employees, y, could be found with the equation y=3(4)xy=3(4)
x where x represents the number of years since the company was founded. How many people founded the company? How can the growth of this company be described?
c. A computer virus is affecting the technology center in such a way that each day , a certain portion of virus-free computers is infected. The number of virus-free computers is recorded in the table. How many computers are in the technology center? What portion of virus-free computers is infected each day? How many computers will remain virus-free at the end of the third day? Justify your answer.
Day Uninfected Computers
0 27
1 18
2 12
d. As part of a major scandal, it was discovered that several statements in the prospectus for ExpoGrow in part (b) were false. If the company actually had five founders and doubles in size each year, what equation should it have printed in its report?