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Advocard [28]
3 years ago
8

what is the growth factor of y=34×4^x, the initial amount of y=15×3^x and the decay factor of y=17×0.2^x

Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
5 0
So the growth factor is the base of the exponential term, so the base of y = 34 * 4^x is 4.
the initial amount is the amount at x = 0
y = 15 * 3^xy = 15 * 3^0y = 15 * 1y = 15 is the initial amount
the decay factor of y=17×0.2^x is same as the growth factor, it is 0.2
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Where:

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{\displaystyle \textstyle {\bar {x}}}= Mean value of the sample

and \sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} } simbolizes the addition of the square of the difference between each observation and the mean value of the sample.

Let's start calculating the mean value:

\bar {x}=\frac{1}{N}  \sum_{i=1}^{N}x_{i}

\bar {x}=\frac{1}{15}*(180+1600+90+140+50+260+400+90+380+110+10+60+20+340+80)

\bar {x}=\frac{1}{15}*(3810)

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Now, let's calculate the summation:

\sum_{i=1}^{N}(x_{i}-\bar {x}) ^{2} }=(180-254)^2+(1600-254)^2+(90-254)^2+...+(80-254)^2

\sum_{i=1}^{N}(x_{i}-\bar {x}) ^{2} }=2173160

So, now we can calculate the standart deviation:

s=\sqrt[ ]{\frac{1}{N-1} \sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} }

s=\sqrt[ ]{\frac{1}{15-1}*(2173160)}

s=\sqrt[ ]{\frac{2173160}{14}}

s=393.99

The sample standard deviation is 393.99

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