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 $(1 \frac{1}{2}) x= \frac{3}{2} x$. So the amount in the jackpot on the next day would be $\frac{3}{2}x+x= \frac{5}{2}x$ dollars.
So the amount in the jackpot on the next day would $\frac{5}{2}$ 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 = $\frac{5}{2} = 2.5 , n = 5.$
Hence,
$4747.50=x\cdot 2.5^{5} \\ 4747.50=97.6563x \\ x=49$ 
Thus x = $49.