Respuesta :
Given:
Daniela gives away some of her marbles every day for five days.
Each day, she has [tex]\dfrac{1}{4}[/tex] the number of marbles she had a previous day.
To find:
The fraction of the original number of marbles Daniela have left after five days.
Solution:
Let the origin number of marble be x.
Number of marbles after one day = [tex]\dfrac{1}{4}x[/tex]
Number of marbles after two days = [tex]\dfrac{1}{4}(\dfrac{1}{4}x)[/tex]
= [tex](\dfrac{1}{4})^2x[/tex]
Similarly,
Number of marbles after three days = [tex](\dfrac{1}{4})^3x[/tex]
Number of marbles after four days = [tex](\dfrac{1}{4})^4x[/tex]
Number of marbles after five days = [tex](\dfrac{1}{4})^5x[/tex]
= [tex]\dfrac{1}{1024}x[/tex]
Since, [tex]\dfrac{1}{1024}[/tex] is multiplied with x, therefore, the number of marbles Daniela have left after five days is [tex]\dfrac{1}{1024}[/tex] part of original number of marbles.
