How do you find a function for this story?

Question

On your first day of work, you get $1. On your second day of work, you get $4. On your third day of work, you get $9. On your fourth day of work, you get $16. It continues this way for 30 days and then once you’ve completed the 30 days you receive a completion bonus of $500,000.

Answer 1

You probably noticed that the pay for each day is the square of the day. Add 'em up and at the end add 500000.

 

final pay = 500000 + ∑ (x_i)^2 as i goes from 1 to 30

where x_i is the ith day

Answer 2

For each day, the amount of money is squared.

 

Let x = day

Let y = amount earned

 

If we put this in a table, you will see what I mean.

 

x  |   y

______

 

1       1

 

2       4

 

3       9

 

4       16

 

 

 

The relationship between x and y is that y is the square of x.  So your function is

 

y = x²

 

 

So if you plug in x=30 into this function, what is the value of y.  The value of y will be amount you earn on the 30 day.