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. Hi 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

@SolomonZelman

Answer 2

@phi

Answer 3

@IMStuck

Answer 4

any idea how we "move" from # of runs in one week to the # of runs in the following week? Do you see a "rule" we could use ?

Answer 5

I see that it multiplies by 4 each week. I'm not sure how to put it into an equation though...

Answer 6

@phi

Answer 7

yes, multiply by 4

we could write the table as

1 4
2 4*4
3 4*4*4

Answer 8

x^y

Answer 9

math is (lots of times) about patterns.

Answer 10

oops. y^x

Answer 11

not any y

Answer 12

if we use exponents to write the table
1 4^1
2 4^2
3 4^3

definitely a pattern. we can predict how many runs if for the nth week, right?

Answer 13

Yep! I could easily do guess and check If I was the manager... heck, I already know the answer is the 5th season.

Answer 14

so to solve this "methodically" we say the number of runs for week "n" is
f(n)= 4^n

we set
4^n= 1024
take the log base 4
n = log_4(1024)
it helps to know 1024 is 2^10 = (2^2)^5 = 4^5
or use a calculator and "change of base"
n= log(1024)/log(4)
where log is base 10

Answer 15

I understand! Thank you yet again @phi ! You always pull through for me.

Answer 16

@1lorax2 How did you get the answer?