Answer:
Fifth Day (1024 pounds)
Step-by-step explanation:
For every subsequent day, he collected 4 times the previous day.
This increase is a ratio/product, therefore the sequence is a geometric sequence.
The nth term of a geometric sequence, [tex]U_n=ar^{n-1}[/tex]
Where:
a=first term
r=common ratio
n=number of terms
Corey collected 4 pounds of newspaper on day 1., a=4
After day one he collected 4 times the amount and for every subsequent day, he collected 4 times the previous day. r=4
We want to determine on which day he will first collect over a 1000 pounds of new paper.
[tex]U_n=1000\\4 X 4^{n-1} =1000\\4^{n-1}=250[/tex]
In order to apply law of indices, we look for the next term greater than 250 which is an index of 4.
[tex]4^{n-1}>256>250\\4^{n-1}>4^4\\n-1>4\\n>4+1\\n>5[/tex]
Therefore on the fifth day, he will collect an amount over 1000 pounds, precisely 1024 pounds.
