Let's go through Jordan's work step by step to identify any errors:
1. The problem states that [tex]\( f \)[/tex] varies inversely as the square root of [tex]\( g \)[/tex]. This can be written mathematically as:
[tex]\[ f \cdot \sqrt{g} = k \][/tex]
where [tex]\( k \)[/tex] is a constant.
2. Jordan starts with the initial values [tex]\( f = 4 \)[/tex] and [tex]\( g = 4 \)[/tex].
3. He correctly uses these values to find the constant [tex]\( k \)[/tex]:
[tex]\[ 4 \cdot \sqrt{4} = k \][/tex]
Solving this:
[tex]\[ 4 \cdot 2 = k \][/tex]
[tex]\[ k = 8 \][/tex]
4. Next, he tries to find the new value of [tex]\( f \)[/tex] when [tex]\( g = 100 \)[/tex]. Using the relationship [tex]\( f \cdot \sqrt{g} = k \)[/tex], with [tex]\( k = 8 \)[/tex]:
[tex]\[ f \cdot \sqrt{100} = 8 \][/tex]
Solving this:
[tex]\[ f \cdot 10 = 8 \][/tex]
[tex]\[ f = \frac{8}{10} \][/tex]
[tex]\[ f = 0.8 \][/tex]
Therefore, the numerical calculations given for finding the new value of [tex]\( f \)[/tex] are correct.
5. However, in Jordan's initial setup before calculating [tex]\( k \)[/tex], he has made a mistake in expressing the inverse variation relationship. The correct relationship for inverse variation should be:
[tex]\[ f = \frac{k}{\sqrt{g}} \][/tex]
Jordan incorrectly uses the relationship as if [tex]\( f \)[/tex] and [tex]\( \sqrt{g} \)[/tex] are directly proportional (i.e., [tex]\( f \cdot \sqrt{g} = \text{constant} \)[/tex]) instead of inversely proportional.
Thus, the first error in Jordan's work is:
A. He used an equation that models direct variation instead of inverse variation.
