Find how many accounts are added from day 0 to 2, from 2 to 4, and from 4 to 6. Are these increases the same, getting steadily larger, or changing irregularly?

After you look at the increases, also compute the ratio of each total to the previous total (for example, $\dfrac{90}{60}$, $\dfrac{135}{90}$, etc.). Are these ratios close to each other?

Decide which type of model matches a situation where, over equal time steps, either the amount added is constant, the pattern of increases matches a squared term, or each value is multiplied by about the same factor.

In the expression line, type: 90-60, 135-90, 202-135 and look at the three numbers Desmos shows. Notice whether these differences are the same or changing.

In a new expression line, type: 90/60, 135/90, 202/135 and examine the three decimal values. See whether these ratios are all close to the same number or quite different from each other.

Based on what you saw—whether the differences were constant, the second differences (differences of those differences) would be constant, or the ratios between terms were roughly constant—choose the model type from the options that describes that behavior.

The table gives:

• Input: days since opening
• Output: total customer accounts

We are asked which type of model (linear, exponential, quadratic, or none) best matches how the total number of accounts changes as days increase.

For a linear growth model, the difference (change) in the output over equal time intervals is constant.

The days increase by 2 each time: $0, 2, 4, 6$. Compute the changes in total accounts over each 2-day interval:

• From day 0 to day 2: $90 - 60 = 30$
• From day 2 to day 4: $135 - 90 = 45$
• From day 4 to day 6: $202 - 135 = 67$

These increases $30, 45, 67$ are not the same, so the relationship is not linear.

For a quadratic growth model, the second differences (the differences of the differences) over equal intervals are constant.

From step 2, the first differences are $30, 45, 67$. Now find the second differences:

• Between $30$ and $45$: $45 - 30 = 15$
• Between $45$ and $67$: $67 - 45 = 22$

The second differences $15$ and $22$ are not equal, so the data do not follow a quadratic pattern.

When a quantity grows by being multiplied by about the same factor over equal time intervals, the ratios between consecutive outputs are roughly constant.

Compute the ratios of each value to the previous one:

• From day 0 to 2: $\dfrac{90}{60} = 1.5$
• From day 2 to 4: $\dfrac{135}{90} = 1.5$
• From day 4 to 6: $\dfrac{202}{135} \approx 1.496$

These ratios are all very close to $1.5$, meaning the total number of accounts is being multiplied by about $1.5$ every 2 days. That pattern is described by an exponential growth model, so choice B) An exponential growth model is correct.