Now we can write a sequence that represents amount of the soup in fluid ounces left after each day. Since 14 of the soup is served, 34 of the soup is left after each day. Therefore, after the first day 1536 fluid ounces of soup is left.
2048 * 3/4= 1536
Let's multiply this number by 34 each time to find the first five terms.
The first five terms of the sequence are 1536, 1152, 864, 648, and 486.
b We see that there is a common ratio of 34 between each pair of consecutive terms. Since a_1= 1536 and r= 34, we can write an equation that represents the nth term of this geometric sequence.
a_n= a_1( r)^(n-1) ⇔ a_n= 1536( 3/4)^(n-1)
c We know that graphs of geometric sequences form an exponential curve when the common ratio is positive. If this common ratio is between 0 and 1, the graph looks like the graph of an exponential decay function.
Recall that the function is never equal to zero since the x-axis is the horizontal asymptote. Similarly, geometric sequences with a common ratio between 0 and 1 cannot be zero. As a result, we can theoretically claim that the soup will never run out. However, in real life, eventually there will not be enough soup to serve.
