Question

A baseball player has been improving every season since making it to the big leagues. Below is a table of the runs he has scored. His manager wants to try to determine when he will score 1024 runs. Explain how to create the exponential function that represents his run-scoring abilities. Then explain how to convert this function into a logarithmic function and why this can help the manager answer his question.

Answer 1

Season       Runs
1                     4
2                     16
3                     64 

f(x) = 4 * 4^x-1 ; where x is the number of seasons.

f(1) = 4 * 4^1-1 ⇒ 4 * 1 = 4
f(2) = 4 * 4^2-1 ⇒ 4 * 4^1 = 16
f(3) = 4 * 4^3-1 ⇒ 4 * 4^2 = 4 *16 = 64
f(4) = 4 * 4^4-1 ⇒ 4 * 4^3 = 4 * 64 = 256
f(5) = 4 * 4^5-1 ⇒ 4 * 4^4 = 4 * 256 = 1024

It would take the baseball player 5 seasons to score 1024 runs.