Answer:
Day 7
Step-by-step explanation:
Given information:
Therefore, each day Celeste has three times as much as she had the previous day.
This can be expressed by the recursive rule:
[tex]\begin{cases}a_n=3a_{n-1}\\a_1=3\end{cases}[/tex]
Therefore:
[tex]\textsf{Day 2}: \quad a_2=3 \cdot a_{1}=3 \cdot 3=9[/tex]
[tex]\textsf{Day 3}: \quad a_3=3 \cdot a_{2}=3 \cdot9=27[/tex]
[tex]\textsf{Day 4}: \quad a_4=3 \cdot a_{3}=3 \cdot 27=81[/tex]
[tex]\textsf{Day 5}: \quad a_5=3 \cdot a_{4}=3 \cdot 81=243[/tex]
[tex]\textsf{Day 6}: \quad a_6=3 \cdot a_{5}=3 \cdot 243=729[/tex]
[tex]\textsf{Day 7}: \quad a_7=3 \cdot a_{6}=3 \cdot 729=2187[/tex]
So the day on which Celeste will have 2,187¢ is day 7.
