Question

In a garden one day Aman observed that her rose garden had one flower. On the second day she observed that there were 3 flowers. On the third she saw 9 flowers and on the fourth day she saw 27 flowers. If this pattern continues how many flowers will be there on the 20th day? Express the answer un exponential form

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{One}\mathrm{first}\mathrm{day},\mathrm{number}\mathrm{of}\mathrm{flower}\mathrm{is}1=3^0 \\ \mathrm{On}\mathrm{second}\mathrm{day},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{flowers}=3=3^1 \\ \mathrm{On}\mathrm{third}\mathrm{day},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{flowers}=9=3^2 \\ \mathrm{On}\mathrm{fourth}\mathrm{day},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{flowers}=27=3^3 \\ \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{flowers}\mathrm{forms}\mathrm{a}\mathrm{pattern}:3^0,3^1,3^2,3^3,\dots \dots \\ \mathrm{Following}\mathrm{the}\mathrm{above}\mathrm{pattern},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{flowers}\mathrm{at}\mathrm{nth}\mathrm{day}\mathrm{is}{3}^{\mathrm{n}-1}. \\ \mathrm{Thus},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{flowers}\mathrm{on}\mathrm{the}20\mathrm{th}\mathrm{day}=3^{20-1}={\mathbf{3}}^{\mathbf{19}} \end{gathered}$$

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