We can see in the graph that for every increment in x, the y-value is halved (that is, multiplied by 1/2).
Since the y-values are being multiplied for every increment of x, we have a geometric sequence or function.
Also, the function has a common ratio, which is the value 1/2 that multiplies y for every increment of x.
Last, we have a recursive formula: each value of y is half of the previous value of y (a_n = (1/2) * a_(n-1))
In order to find the explicit formula, since we have an exponential function, we can use the model y = a*b^x.
Using the points (1, 32) and (2, 16), we have:
[tex]\begin{gathered} 32=a\cdot b^1\to a=\frac{32}{b} \\ 16=a\cdot b^2\to b^2=\frac{16}{a}=\frac{16b}{32}\to b=\frac{1}{2} \\ 32=a\cdot\frac{1}{2}\to a=64 \end{gathered}[/tex]
So the explicit function is y = 64 * (1/2)^x.
Looking at the graph, the 5th term of the sequence (x = 5) is found by halving the value y = 8 two times, so the 5th term is 2.
