If a rookie in the NBA asked to be paid 1 dollar his first year, 2 dollars his 2nd year, 4 dollars his third year, 8 dollars his fourth year, etc. at what year would he meet/exceed Michael Jordan who gets 1 million dollars a year?
Using a table and graph, find the general expressions for the rookie and for Michael Jordan's salaries. What does each of these representations (table, graph, general expression) add to your understanding on the problem?
What pattern do you observe below? Discuss the possibilities for why 2^0 is equal to 1.
2^0 = 1, 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16 . . .
Find a general expression for this pattern and graph it. What happens if you use other bases (e.g. 3, 4...)? What is the same? What is different? What if you use negative exponents?
Investigate the pattern for b^n when 0 < b < 1. Compare b^n with (1/b)^n using tables and graphs.