Answer:
Option 1st is correct
\(f(n) = 16 \cdot (0.5)^{n-1}\)
Step-by-step explanation:
The nth term for the geometric sequence is given by:
\(f(n)=f(1) \cdot r^{n-1}\) ....[1]
where,
\(f(1)\) is the first term
r is the common ratio of the terms.
n is the number of terms.
As per the statement:
Midge added some chlorine to the water in a pool. The chlorine evaporated at a fixed rate every week.
The table below shows the amount of chlorine f(n), in ounces, that was left in the pool after n weeks:
n f(n)
1 16
2 8
3 4
4 2
This is an geometric sequence
For n = 1
From the table:
\(f(1) = 16\)
r = 0.5
Since,
\(\frac{f(2)}{f(1)} = \frac{8}{16} = 0.5\),
\(\frac{f(3)}{f(2)} = \frac{4}{8} = 0.5\), and so on..
Substitute the value of f(1) = 16 and r = 0.5 in [1] we have;
\(f(n) = 16 \cdot (0.5)^{n-1}\)
Therefore, the function best shows the relationship between n and f(n) is, \(f(n) = 16 \cdot (0.5)^{n-1}\)
