Final answer:
To write an expression for a in terms of b when a is inversely proportional to b², we use the formula a = k/b², where k is the constant of variation. Substituting the given values of a and b, we can solve for k and obtain the expression a = 72/b².
Step-by-step explanation:
To write an expression for a in terms of b when a is inversely proportional to b², we can use the formula for inverse variation: a = k/b², where k is the constant of variation.
We can find the value of k by substituting the given values of a and b into the equation. When b = 4 and a = 4.5, we have: 4.5 = k/4².
Solving this equation, we get k = 4.5 × 4² = 72.
Therefore, the expression for a in terms of b is a = 72/b².