Answer:
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Step-by-step explanation:
Answer:
Step-by-step explanation:
There were 1000 trees in the first year and every year new trees are getting added.
The sequence formed for the new trees every year is
Year 1 2 3
New trees 1000 200 40
We see a geometric sequence has been formed by the new trees added
Ratio of the second year and 1st year trees added = ![\frac{200}{1000}=\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B200%7D%7B1000%7D%3D%5Cfrac%7B1%7D%7B5%7D)
Similarly ratio of trees added in 3rd year to 2nd year = ![\frac{40}{200}=\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B40%7D%7B200%7D%3D%5Cfrac%7B1%7D%7B5%7D)
So there is a common ratio of ![\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D)
Explicit formula of a geometric sequence representing growth of the trees by
![T_{n}=a(r)^{n-1}](https://tex.z-dn.net/?f=T_%7Bn%7D%3Da%28r%29%5E%7Bn-1%7D)
where a = number of trees grown first year
r = common ratio
n = number of years
Explicit formula showing the growth of the trees using sigma notation will be
![\sum_{n=1}^{\infty}1000(\frac{1}{5})^{n-1}](https://tex.z-dn.net/?f=%5Csum_%7Bn%3D1%7D%5E%7B%5Cinfty%7D1000%28%5Cfrac%7B1%7D%7B5%7D%29%5E%7Bn-1%7D)
And Formula for number of trees every year will be
![\sum_{n=1}^{\infty}1000+1000(\frac{1}{5})^{n-1}](https://tex.z-dn.net/?f=%5Csum_%7Bn%3D1%7D%5E%7B%5Cinfty%7D1000%2B1000%28%5Cfrac%7B1%7D%7B5%7D%29%5E%7Bn-1%7D)
![\sum_{n=1}^{\infty}1000[1+(\frac{1}{5})^{n-1}]](https://tex.z-dn.net/?f=%5Csum_%7Bn%3D1%7D%5E%7B%5Cinfty%7D1000%5B1%2B%28%5Cfrac%7B1%7D%7B5%7D%29%5E%7Bn-1%7D%5D)
Sum of the trees will be
![S=\frac{a}{1-r}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7Ba%7D%7B1-r%7D)
= ![\frac{2000}{1-\frac{1}{5}}](https://tex.z-dn.net/?f=%5Cfrac%7B2000%7D%7B1-%5Cfrac%7B1%7D%7B5%7D%7D)
= ![\frac{2000}{\frac{4}{5} }](https://tex.z-dn.net/?f=%5Cfrac%7B2000%7D%7B%5Cfrac%7B4%7D%7B5%7D%20%7D)
= ![\frac{2000\times 5}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B2000%5Ctimes%205%7D%7B4%7D)
= 2500
The answer would be D. Remember time is always on the x axis and the independent variable is always on the y
The decimal equivalent of 3/10 is .3
Answer:
14/26
Step-by-step explanation:
6+8=14
14+12=26