Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 192689 by sciencestudentW last updated on 24/May/23

a plant grow up 1.67cm in the first week after that it grow up 4% grow up more than the first week every week, how much will grow up in 11th week?

$${a}\:{plant}\:{grow}\:{up}\:\mathrm{1}.\mathrm{67}{cm}\:{in}\:{the}\:{first}\:{week} \\ $$$${after}\:{that}\:{it}\:{grow}\:{up}\:\mathrm{4\%}\:{grow}\:{up}\:{more} \\ $$$${than}\:{the}\:{first}\:{week}\:{every}\:{week},\:{how}\:{much} \\ $$$${will}\:{grow}\:{up}\:{in}\:\mathrm{11}{th}\:{week}? \\ $$

Commented by sciencestudentW last updated on 24/May/23

?

$$? \\ $$

Answered by Skabetix last updated on 24/May/23

It remains 11−1=10 weeks geometrical sequence the 11^(th) week the plant will grow up : 1.67×(1.04)^(10) ≈2.47 cm

$${It}\:{remains}\:\mathrm{11}−\mathrm{1}=\mathrm{10}\:{weeks} \\ $$$$\boldsymbol{{geome}}{trical}\:\boldsymbol{\mathrm{se}}{que}\boldsymbol{\mathrm{nce}} \\ $$$$\boldsymbol{\mathrm{the}}\:\mathrm{11}^{\boldsymbol{\mathrm{th}}} \:\boldsymbol{\mathrm{week}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{plant}}\:\boldsymbol{\mathrm{will}}\:\boldsymbol{\mathrm{grow}}\:\boldsymbol{\mathrm{up}}\:: \\ $$$$\mathrm{1}.\mathrm{67}×\left(\mathrm{1}.\mathrm{04}\right)^{\mathrm{10}} \approx\mathrm{2}.\mathrm{47}\:{cm} \\ $$

Commented by sciencestudentW last updated on 25/May/23

thanks great solotion! the total hieght of plant in all 11 week will be 1.67×(1.04)^1 +1.67×(1.04)×10^2 +...+1.67×(1.04)^(10) ? ok?

$${thanks}\:{great}\:{solotion}! \\ $$$${the}\:{total}\:{hieght}\:{of}\:{plant}\:{in}\:{all}\:\mathrm{11}\:{week} \\ $$$${will}\:{be}\:\mathrm{1}.\mathrm{67}×\left(\mathrm{1}.\mathrm{04}\right)^{\mathrm{1}} +\mathrm{1}.\mathrm{67}×\left(\mathrm{1}.\mathrm{04}\right)×\mathrm{10}^{\mathrm{2}} +...+\mathrm{1}.\mathrm{67}×\left(\mathrm{1}.\mathrm{04}\right)^{\mathrm{10}} ?\:\:{ok}? \\ $$

Answered by manxsol last updated on 25/May/23

determinant ((1,(1.67×1.04^0 )),(2,(1.67×1.04^1 )),(3,(1.67×1.04^2 )),(,),(,),(,),(,),((11),(1.67×1.04^(10) )),(n,(1.67×1.04^(n−1) )),(Σ_1 ^(11) ,(1.67 (((1.04^(11) −1)/(1.04−1)))))) 1.67 (((1.04^(11) −1)/(1.04−1))) 22.522207 n=11 r=1.04 a_1 =1.67 Σprogresion geometric= a_1 (((r^n −1))/(r−1))

$$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}{\mathrm{1}}&\hline{\mathrm{1}.\mathrm{67}×\mathrm{1}.\mathrm{04}^{\mathrm{0}} }\\{\mathrm{2}}&\hline{\mathrm{1}.\mathrm{67}×\mathrm{1}.\mathrm{04}^{\mathrm{1}} }\\{\mathrm{3}}&\hline{\mathrm{1}.\mathrm{67}×\mathrm{1}.\mathrm{04}^{\mathrm{2}} }\\{}&\hline{}\\{}&\hline{}\\{}&\hline{}\\{}&\hline{}\\{\mathrm{11}}&\hline{\mathrm{1}.\mathrm{67}×\mathrm{1}.\mathrm{04}^{\mathrm{10}} }\\{{n}}&\hline{\mathrm{1}.\mathrm{67}×\mathrm{1}.\mathrm{04}^{{n}−\mathrm{1}} }\\{\sum_{\mathrm{1}} ^{\mathrm{11}} }&\hline{\mathrm{1}.\mathrm{67}\:\left(\frac{\mathrm{1}.\mathrm{04}^{\mathrm{11}} −\mathrm{1}}{\mathrm{1}.\mathrm{04}−\mathrm{1}}\right)}\\\hline\end{array} \\ $$$$\mathrm{1}.\mathrm{67}\:\left(\frac{\mathrm{1}.\mathrm{04}^{\mathrm{11}} −\mathrm{1}}{\mathrm{1}.\mathrm{04}−\mathrm{1}}\right) \\ $$$$\mathrm{22}.\mathrm{522207} \\ $$$${n}=\mathrm{11} \\ $$$${r}=\mathrm{1}.\mathrm{04} \\ $$$${a}_{\mathrm{1}} =\mathrm{1}.\mathrm{67} \\ $$$$\Sigma{progresion}\:{geometric}= \\ $$$${a}_{\mathrm{1}} \frac{\left({r}^{{n}} −\mathrm{1}\right)}{{r}−\mathrm{1}} \\ $$$$ \\ $$

Commented by sciencestudentW last updated on 28/May/23

nice

$${nice} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com