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anonymous
 one year ago
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 243 runs. Explain how to create the exponential function that represents his runscoring abilities. Then explain how to convert this function into a logarithmic function and why this can help the manager answer his question.
anonymous
 one year ago
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 243 runs. Explain how to create the exponential function that represents his runscoring abilities. Then explain how to convert this function into a logarithmic function and why this can help the manager answer his question.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433630314852:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910 can you help?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Concentrationalizing can you?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, a general exponential function would look like \(a^{x}\). Given that, let's see if we can try and determined what our avalue would be based on the chart you have. The season will represent xvalues and the runs will represent yvalues. So if we plug those values in: \(a^{1} = 3\) \(a^{2} = 9\) \(a^{3} = 27\) So what would a be?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a would be 3, right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Right. So we can say our function is \(y = a^{x}\). Now do you know how to change an exponential equation into a logarithmic one?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay. Let's use this idea then. \(log_{b}m = x \implies\ b^{x} = m\) Maybe you've seen that connection between exponentials and logarithms before.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Either way, you can kind of see how the variables in that identity switch around when you want to change from a logarithm to an exponential and viceversa

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So in the logarithm would b be 3?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And then you could say y would take the place of m, so that would give you \(log_{3}y = x\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the identity above would be your explanation as to why you can claim that this logarithmic function works. As for funding your answer, that comes down to solving for x in the equation \(3^{x} = 243\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0x would be 5\[3^{5}=243\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yep, so 5 seasons to score 243 runs.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, I think I understand now. Thank you :)
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