Answer:
[tex]b=\dfrac{1}{5}a[/tex].
Step-by-step explanation:
We need to write an equation for the amount of chemical B as a function of the amount of chemical A.
[tex]b=f(a)[/tex]
[tex]b\propto a[/tex]
[tex]b=ka[/tex] ...(1)
where, k is constant of proportionality.
It is given that fifteen grams of chemical A is used to produce 3 grams of chemical B. It means a=15 and b=3.
Substitute a=15 and b=3 in (1).
[tex]3=k(15)[/tex]
[tex]k=\dfrac{3}{15}=\dfrac{1}{5}[/tex]
Substitute [tex]k=\dfrac{1}{5}[/tex] in (1).
[tex]b=\dfrac{1}{5}a[/tex]
Therefore, the required function is [tex]b=\dfrac{1}{5}a[/tex].
