Question

write as a power function:
m varies directly with the cube of q
and m is 81 when q is 3.

m = ?q^

Explanation:

Step1: Recall direct variation formula

For direct variation, if \( m \) varies directly with the cube of \( q \), the formula is \( m = kq^3 \), where \( k \) is the constant of variation.

Step2: Substitute known values

We know \( m = 81 \) when \( q = 3 \). Substitute into the formula: \( 81 = k(3)^3 \).

Step3: Solve for \( k \)

First, calculate \( 3^3 = 27 \). Then the equation becomes \( 81 = 27k \). Divide both sides by 27: \( k=\frac{81}{27}=3 \).

Step4: Write the power function

Substitute \( k = 3 \) back into \( m = kq^3 \), so \( m = 3q^3 \).

Answer:

\( m = 3q^3 \) (so the first box is 3 and the exponent box is 3)