Question

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 please.

Answer 1

The initial amount in the jackpot was x dollars. The amount added to the jackpot was
`(1 (1)/(2)) x= (3)/(2) x`. So the amount in the jackpot on the next day would be
`(3)/(2)x+x= (5)/(2)x` dollars.
So the amount in the jackpot on the next day would
`(5)/(2)` of the previous day. This can be modeled by a geometric sequence with the following formula


`A=x \cdot r^(n)`
where A = amount in future,
x = initial amount,
r = rate of change,
n= number of days.

In this case, A = 4747.50, r =
`(5)/(2) = 2.5 , n = 5.`
Hence,

`4747.50=x\cdot 2.5^(5) \\ 4747.50=97.6563x \\ x=49`
Thus x = $49.