From the given data, we observe that the amount of water dripping from the faucet into the bowl increases steadily with time, indicating a direct proportionality between time and the amount of water.
a) The constant of proportionality, often denoted as k, represents the relationship between the two variables. In this case, it signifies the amount of water collected (in milliliters) per unit time (in seconds). We can find the value of k by taking the ratio of the number of milliliters to the time in seconds from any given pair of corresponding values in the data. Here, we'll use the first pair: 10 milliliters and 2 seconds. Thus, k = 10 / 2 = 5.0. This means every second, 5 milliliters of water drip into the bowl from the faucet.
b) Now, to model this relationship mathematically i.e., to establish an equation using this constant proportionality, we simply use the formula y = k * x. Here, x represents the time in seconds, k is the constant of proportionality we found previously, and y is the number of milliliters of water in the bowl.
Substitute the value of k into the equation, we get y = 5.0 * x.
Therefore, the equation representing the relationship between the time and the amount of water collected is y = 5.0 * x. This indicates that for each second, the amount of water in the bowl increases by 5 milliliters.