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 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. @Directrix @campbell_st @Abhisar @jdoe0001 @e.mccormick @SithsAndGiggles @TheSmartOne @Whitemonsterbunny17 @Nnesha @tHe_FiZ

Answer 1

@tHe_FiZiCx99

Answer 2

First, do you know what the exponential function is?

Answer 3

Season Runs

1 2

2 4

3 8

Answer 4

it's when a function whose value is a constant raised to the power of the argument and especially the function where the constant is e.

Answer 5

Yes, "a exponential function" is some number to the power of x, so \(a^x\). "THE exponential function" is \(e^x\), as in it is the only one where that is the specific name.

Now, I am emphasizing the "the" a bt more than needed, but you get the point.


Anyhow, some exponenial function represents those scores.

Answer 6

right

Answer 7

So your general form is:

\(y=a^x\)

You have been given some numbers for x and y. If you put them in, you can solve for a.

Answer 8

idk which one is y and which is x.

Answer 9

Look at the way I graphed it. Which is on the x axis and which is on the y?

Answer 10

so 2= a^1?

Answer 11

Yep! Which means a= what?

Answer 12

2

Answer 13

OK, so put 2 in for a and test with one of the other values to confirm.

Answer 14

is that all i have to do for this question?

Answer 15

Well, you have to describe the process, but yes. Those are the basic steps.

Answer 16

Can you help me describe the process?

Answer 17

@e.mccormick

Answer 18

Well, type up what you did as a descripton and I'll look at it.

Answer 19

k