Pretend there are 100 visits at the start. What would the number of visits be after 1 hour and after 2 hours if it increases by 15% each hour? Do the amounts you add each hour stay the same or change?

One model type has a constant difference between successive values; the other has a constant ratio (you keep multiplying by the same factor). Which situation fits "increases by about 15% each hour"?

Since the visits are increasing over time, eliminate any options that describe a decreasing pattern.

In Desmos, type an expression like $y_1 = 100(1.15)^x$ to represent a situation where you start with 100 visits and the total is multiplied by $1.15$ each hour (a 15% increase of the current amount). Look at how the graph changes as $x$ (time) increases.

Now type $y_2 = 100 + 15x$ to represent adding 15 visits every hour. Use a table (tap the gear icon, then the table icon) or just look at the graph to see how $y_1$ and $y_2$ change from one hour to the next: in one model, the difference between hours is constant; in the other, the percentage change is constant.

Compare the two patterns: one shows equal jumps in visits each hour; the other shows jumps that get larger as the total grows. Decide which type of pattern fits the idea "increases by about 15% each hour," and then choose the option that names that type of model.

We are modeling the total number of website visits as time (in hours) passes after the advertisement goes live.

So we want a function where:

• Input: time in hours
• Output: total number of visits so far

The key is to understand how the visits change from hour to hour.

"Increases by about 15% each hour" means that each hour, the new total is 15% more than the previous total, not 15 more visits.

If at some hour there are $100$ visits, then after 1 more hour there would be:

• $100 + 0.15 \times 100 = 115$ visits.

After another hour, we take 15% of 115, not 100:

• $115 + 0.15 \times 115 = 132.25$ visits.

So each step multiplies the current amount by $1.15$ (because $1 + 0.15 = 1.15$).

A linear model adds or subtracts the same number each hour (constant amount of change). For example, $+20$ visits every hour.

Here, the problem describes a constant percent change each hour (15% of the current value), so the amount added each hour keeps getting larger as the total grows.

This kind of "multiply by the same factor each step" behavior is not linear; it is the other common type of model used for repeated percentage changes.

The problem says the number of visits increases each hour, so the function must:

• Go up as time increases (not down), and
• Represent repeated percentage increases.

That rules out any model that has a decreasing pattern (negative slope or decay). The remaining option that matches an increasing function with repeated percentage change is an exponential growth model (Choice C).