Question

**Comparing the two experiments, will there ever be more mold on the muffin than on the bread? Explain in at least 4 sentences how you came to your conclusion using our key understanding from today's class.

Answer 1

Experiment ONE:

We can model the equation linearly. The linear form is:

$y=mx+b$

Where

m is the slope (or, rate)

b is the y-intercept (or, initial value)

Given, the initial value is "50", we can say b = 50.

The mold triples with each observation. So, the rate (m) is 3.

Thus, the equation to model this situation is:

$y=3x+50$

Experiment TWO:

We can also model this situation linearly.

This situation is an easier one. The number of molds increase by 8 with each observation. So, the rate (m) is "8".

The initial value (b) is "12".

So, we can model the equation:

$y=8x+12$

To find out if mold on muffin will ever be greater than mold on bread, we can write:

$8x+12>3x+50$

Let's solve for x:

$\begin{gathered} 8x+12>3x+50 \\ 8x-3x>50-12 \\ 5x>38 \\ x>\frac{38}{5} \\ x>7\frac{3}{5} \end{gathered}$

So, from 8 observation onwards, the amount of mold on the muffin will be greater than the amount of mold on the bread.