On each day of a contest, the amount of money added to the jackpot was one and one-half times the total from the previous day. the initial amount in the jackpot was x dollars. after five days, the total amount in the jackpot was $4,747.50. to the nearest dollar, what was the value of x? derive the formula and show your work .

The initial amount in the jackpot was x dollars. The amount added to the jackpot was . So the amount in the jackpot on the next day would be  dollars.
So the amount in the jackpot on the next day would  of the previous day. This can be modeled by a geometric sequence with the following formula


where A = amount in future,
x = initial amount,
r = rate of change,
n= number of days.

In this case, A = 4747.50, r = 
Hence,
 
Thus x = $49.