Question

Corey collection 4pound of newspaper on day 1after day one he collected 4 times the amount on which day did he first collect over a 1000 pounds of new paper

Answer 1

Fifth Day (1024 pounds)

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,
`U_n=ar^(n-1)`

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.

`U_n=1000\\4 X 4^(n-1) =1000\\4^(n-1)=250`

In order to apply law of indices, we look for the next term greater than 250 which is an index of 4.

`4^(n-1)>256>250\\4^(n-1)>4^4\\n-1>4\\n>4+1\\n>5`

Therefore on the fifth day, he will collect an amount over 1000 pounds, precisely 1024 pounds.