Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Feb 25, 2024

Construct a function that expresses the relationship between your test grade $P$ and study hours $s$ , where $P = k \cdot s$ .

STEP 1

Assumptions
1. The relationship between the grade on the test ( $P$ ) and the number of hours studied ( $s$ ) is a direct variation.
2. The constant of variation is represented by $\mathrm{k}$ .
3. The function we are constructing will express $P$ in terms of $s$ and $\mathrm{k}$ .

STEP 2

Understand the definition of direct variation. A direct variation between two variables means that as one variable increases, the other variable increases at a constant rate. This can be expressed by the equation:
$P = \mathrm{k} \cdot s$

STEP 3

Use the given variables to write the function that expresses the direct relationship between the grade on the test ( $P$ ) and the number of hours studied ( $s$ ), with $\mathrm{k}$ as the constant of variation.
$P(s) = \mathrm{k} \cdot s$
This function shows that the grade on the next test, $P$ , is directly proportional to the number of hours studied, $s$ , with $\mathrm{k}$ being the proportionality constant.

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