Question

Or

Sebastian uses his phone primarily to take a lot of selfies. The storage space on his phone is limited, so Sebastian needs to keep track of how many selfies he takes.
There is a proportional relationship between the number of selfies Sebastian takes, x, and the amount of storage (in megabytes) he uses taking selfies, y.

Answer 1

The statement suggests that there is a proportional relationship between the number of selfies Sebastian takes, x, and the amount of storage (in megabytes) he uses taking selfies, y. This means that if we were to graph the number of selfies taken, x, on the x-axis and the amount of storage used, y, on the y-axis, the points would fall on a straight line and the slope of the line would be a constant.

In mathematical terms, we can represent this proportional relationship as y = kx, where k is the proportionality constant, or the constant of proportionality. This equation states that the amount of storage used, y, is directly proportional to the number of selfies taken, x.

Answer 2

Sebastian's use of storage for selfies demonstrates a linear relationship, where the amount of storage space used increases at a constant rate with the number of selfies taken, and can be modeled with a linear equation, unlike inverse or exponential relationships.

Step-by-step explanation:

The question is related to a proportional relationship between the number of selfies (x) and the storage space used (y) on Sebastian's phone. This is an example of a linear relationship where the variables change at a constant rate.

To represent this relationship mathematically, one could use a linear equation of the form y = mx where m is the constant of proportionality that relates the number of selfies to the megabytes used. If we knew the average size of one selfie, we could determine m. Then, Sebastian could use this information to keep track of his phone's storage capacity.

In contrast, an inverse proportional relationship is expressed by an equation of the form y = k/x. Here, as the number of selfies x increases, the value of y would decrease, assuming k stays the same. This is not the case for Sebastian as the more selfies he takes, the more storage space he uses.

Exponential relationships describe situations where a change in the independent variable (x) produces a proportional change in the dependent variable (y), and as y gets larger, its rate of growth also increases. This does not apply to Sebastian's situation as the growth in the use of storage is consistent (linear), not increasing at an increasing rate like bacterial growth under ideal conditions.