Subtract consecutive counts (for example, $100-50$, then $200-100$). Are you adding the same amount each time?

Now divide consecutive counts (for example, $100 \div 50$, then $200 \div 100$). Are you multiplying by about the same number each time?

Decide whether the pattern looks like a straight-line change (constant addition), a repeated multiplication pattern, or no clear pattern at all.

In Desmos, create a table (using something like x1 for time and y1 for bacteria). Enter the points: $(0,50)$, $(5,100)$, $(10,200)$, $(15,400)$, and $(20,800)$.

Check whether the plotted points lie roughly on a straight line or if they curve upward more and more steeply as $x$ increases. A straight-line pattern would suggest a linear model; a rapidly curving pattern suggests a different type of model.

In Desmos, you can try typing a linear regression like y1 ~ m x1 + b and an exponential regression like y1 ~ a b^{x1}. Compare how well each type of equation fits the plotted points to decide which model type from the choices best matches the data.

List the data pairs as $(\text{time}, \text{bacteria})$:

• $(0, 50)$
• $(5, 100)$
• $(10, 200)$
• $(15, 400)$
• $(20, 800)$

We want to see what kind of relationship connects time to bacteria count.

Find how much the bacteria count changes every 5 minutes:

• From 50 to 100: $+50$
• From 100 to 200: $+100$
• From 200 to 400: $+200$
• From 400 to 800: $+400$

These differences are not constant, so the relationship is not linear (neither increasing linear nor decreasing linear).

Now look at how each count compares to the previous one:

• $100 \div 50 = 2$
• $200 \div 100 = 2$
• $400 \div 200 = 2$
• $800 \div 400 = 2$

Each time, the bacteria count is multiplied by $2$ over the same time interval (5 minutes). This is the key sign of exponential behavior.

Because the bacteria count is increasing and does so by a constant factor (doubling every 5 minutes), the best model is an increasing exponential function. So the correct answer is C) Increasing exponential.