Answer :
Given:
Initial number of pieces Myra have = 800.
Every 5 days she places one quarter of the remaining pieces into the puzzle.
To find:
The number of remaining pieces after 23 days.
Solution:
Initial number of pieces Myra have = 800.
Every 5 days she places one quarter of the remaining pieces into the puzzle.
It means, she will place the puzzles on 5,10,15,20,25,.. days. she will place the puzzle 4 times before 23 days.
The number of remaining pieces decreasing by [tex]\dfrac{1}{4}[/tex].
Formula for number of remaining pieces is
[tex]y=a_0(1-r)^t[/tex]
where, [tex]a_0[/tex] is the initial value, r is decreasing rate and t is time.
Putting [tex]a_0=800,r=\dfrac{1}{4}[/tex] and t=4, we get
[tex]y=800(1-\dfrac{1}{4})^4[/tex]
[tex]y=800(\dfrac{3}{4})^4[/tex]
[tex]y=800(0.75)^4[/tex]
[tex]y=800(0.31640625 )[/tex]
[tex]y=253.125[/tex]
Approximate the value to the nearest whole number.
[tex]y\approx 253[/tex]
Therefore, the number of remaining pieces is 253.