Find the relationship between the number of black dots and grey dots and calculate the number of grey dots for 1, 2, 3, and 4 black dots.

To solve this problem, we first need to identify the pattern relating the number of black dots to the number of grey dots.

Step 1: Analyze the given patterns to find the number of grey dots for each number of black dots.

• For 1 black dot (first pattern), there are 8 grey dots.
• For 2 black dots (second pattern), there are 12 grey dots.
• For 3 black dots (third pattern), there are 16 grey dots.
• For 4 black dots (fourth pattern), there are 20 grey dots.

Step 2: Determine the relationship.
Let $n$ be the number of black dots and $G$ be the number of grey dots.
We observe that as $n$ increases by 1, $G$ increases by 4 ($12-8=4$, $16-12=4$, $20-16=4$). This indicates a linear relationship of the form $G = mn + c$, where $m=4$.
Using the first data point ($n=1, G=8$):

$$8 = 4(1) + c$$ $$8 = 4 + c$$ $$c = 4$$

So, the formula describing the relationship is $G = 4n + 4$.

Now, we use this formula to answer each question.