Answer:
The percent change in runs batted in from 2001 to 2008 is 26.47%
Step-by-step explanation:
The number of runs chipper batted in the year 2001 = 102 runs
The number of runs chipper batted in the year 2008 = 75 runs
Here, so the Change in the runs batted
= Runs Batted in year 2001 - Runs batted in the year 2008
= 102 runs - 75 runs = 27 runs
Now, The percentage change in the run = ![= \frac{\textrm{Change in the batted run from 2001 to 2008}}{\textrm{Total number of batted runs in 2001}} \times 100](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B%5Ctextrm%7BChange%20in%20the%20batted%20run%20from%202001%20to%202008%7D%7D%7B%5Ctextrm%7BTotal%20number%20of%20batted%20runs%20in%202001%7D%7D%20%20%5Ctimes%20100)
= ![\frac{27}{102} \times 100 = 26.47](https://tex.z-dn.net/?f=%5Cfrac%7B27%7D%7B102%7D%20%20%5Ctimes%20100%20%3D%2026.47)
or, The percentage change = 26.47%
Hence, the percent change in runs batted in from 2001 to 2008 is 26.47%
since this is a multiplication, all the numerators are just factors of the product numerator and all denominators are just factors of the product denominator, so we can simply reorder them some, without changing the product.
![\bf \cfrac{7}{8}\times \cfrac{4}{15}\times \cfrac{3}{7}\implies \cfrac{7}{7}\times \cfrac{4}{8}\times \cfrac{3}{15}\implies \cfrac{1}{1}\times \cfrac{1}{2}\times \cfrac{1}{5}\implies \cfrac{1\cdot 1\cdot 1}{1\cdot 2\cdot 5}\implies \cfrac{1}{10}](https://tex.z-dn.net/?f=%20%5Cbf%20%5Ccfrac%7B7%7D%7B8%7D%5Ctimes%20%5Ccfrac%7B4%7D%7B15%7D%5Ctimes%20%5Ccfrac%7B3%7D%7B7%7D%5Cimplies%20%5Ccfrac%7B7%7D%7B7%7D%5Ctimes%20%5Ccfrac%7B4%7D%7B8%7D%5Ctimes%20%5Ccfrac%7B3%7D%7B15%7D%5Cimplies%20%5Ccfrac%7B1%7D%7B1%7D%5Ctimes%20%5Ccfrac%7B1%7D%7B2%7D%5Ctimes%20%5Ccfrac%7B1%7D%7B5%7D%5Cimplies%20%5Ccfrac%7B1%5Ccdot%201%5Ccdot%201%7D%7B1%5Ccdot%202%5Ccdot%205%7D%5Cimplies%20%5Ccfrac%7B1%7D%7B10%7D%20)
The table models an exponential relationship, and the equation of the table is ![y = 4(1/2)^x](https://tex.z-dn.net/?f=y%20%3D%204%281%2F2%29%5Ex)
<h3>How to analyze the table of values?</h3>
The table of values is given as:
x 0 1 2 3 4
y 4 2 1 1/2 1/4
The above table shows an exponential model
An exponential model is represented as:
![y = ab^x](https://tex.z-dn.net/?f=y%20%3D%20ab%5Ex)
When x = 0 and y = 4, we have
![ab^0 = 4](https://tex.z-dn.net/?f=ab%5E0%20%3D%204)
Evaluate
a = 4
When x = 1 and y = 2, we have
![ab^1 = 2](https://tex.z-dn.net/?f=ab%5E1%20%20%3D%202)
Evaluate
![ab = 2](https://tex.z-dn.net/?f=ab%20%20%3D%202)
Substitute 4 for a
4b = 2
Divide both sides by 4
b = 1/2
Substitute 4 for a and 1/2 for b in ![y = ab^x](https://tex.z-dn.net/?f=y%20%3D%20ab%5Ex)
![y = 4(1/2)^x](https://tex.z-dn.net/?f=y%20%3D%204%281%2F2%29%5Ex)
Hence, the equation of the table is ![y = 4(1/2)^x](https://tex.z-dn.net/?f=y%20%3D%204%281%2F2%29%5Ex)
Read more about exponential models at:
brainly.com/question/11464095
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