when the weight of apples is increased by a factor of 4, by what factor does the total cost increase?

Explanation:

Step1: Find the relationship between weight and cost

Let the weight be (w) and the cost be (c). From the table, when (w = 1), (c=2); when (w = 4), (c = 8); when (w=6), (c = 12); when (w = 10), (c=20). We can see that the relationship is (c = 2w) (since (\frac{c}{w}=\frac{2}{1}=\frac{8}{4}=\frac{12}{6}=\frac{20}{10}=2)).

Step2: Analyze the effect of increasing weight by a factor

If the original weight is (w_1) and the new weight is (w_2=4w_1). The original cost (c_1 = 2w_1), and the new cost (c_2=2w_2). Substitute (w_2 = 4w_1) into (c_2), we get (c_2=2\times(4w_1)=4\times(2w_1)=4c_1)

Answer:

(4)