SOLUTION: 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 wil

Question 1010859: 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 256 runs.

Season runs
1 2
2 4
3 8

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. please use details.

Found 2 solutions by rothauserc, fractalier:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Observe that
y = 2^x is the number of runs scored(y) where x is the season (1, 2, 3, .....)
using logarithm definition
x = log (base 2) of y
******************************************************************************
we are given y = 256, therefore
x = log (base 2) of 256
x = 8
the baseball player will score 256 runs in his 8th season

Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
His run total is 2^(season #)...thus 2^8 = 256...his eighth season...
Since his total goes up by a factor of two each year, we have
, a simple exponential function.
Taking the log to the base two of each side, we get
and

By taking the log to the base two of 256, he gets 8.
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