Question

if r varies inversely as t and r = 4 when t = 24, write the equation of a proportional model and find the constant of proportionality, k. move the correct answer to each box. each answer may be used more than once. step 1: label input/output. step 2: write equation

Explanation:

Step1: Recall inverse - variation formula

The formula for inverse variation is $R=\frac{k}{T}$, where $k$ is the constant of proportionality.

Step2: Substitute given values to find $k$

We know that $R = 4$ when $T=24$. Substitute these values into $R=\frac{k}{T}$: $4=\frac{k}{24}$.

Step3: Solve for $k$

Multiply both sides of the equation $4=\frac{k}{24}$ by 24. So, $k = 4\times24=96$.

Step4: Write the final equation

The equation of the proportional model is $R=\frac{96}{T}$.

Answer:

The equation of the proportional model is $R=\frac{96}{T}$ and the constant of proportionality $k = 96$.