52. (fif: question 12)\nthe restaurant pizza by the π offers six sizes: personal (8 in), small (10 in)…

52. (fif: question 12)\nthe restaurant pizza by the π offers six sizes: personal (8 in), small (10 in), medium (12 in), large (14 in), extra - large (16 in), and π - zilla (24 in). the table below shows the cost of a cheese pizza as a function of the diameter of the pizza.\n|diameter (inches)|cost|\n|----|----|\n|8|$6.99|\n|10|$9.49|\n|12|$10.99|\n|14|$11.79|\n|16|$13.99|\n|24|$25.99|\npart a: what is the average rate of change in cost when moving from a medium pizza to a π - zilla?\na. $0.79\nb. $1.25\nc. $1.49\nd. $1.99\npart b: what does this value mean in the context of this problem?

52. (fif: question 12)\nthe restaurant pizza by the π offers six sizes: personal (8 in), small (10 in), medium (12 in), large (14 in), extra - large (16 in), and π - zilla (24 in). the table below shows the cost of a cheese pizza as a function of the diameter of the pizza.\n|diameter (inches)|cost|\n|----|----|\n|8|$6.99|\n|10|$9.49|\n|12|$10.99|\n|14|$11.79|\n|16|$13.99|\n|24|$25.99|\npart a: what is the average rate of change in cost when moving from a medium pizza to a π - zilla?\na. $0.79\nb. $1.25\nc. $1.49\nd. $1.99\npart b: what does this value mean in the context of this problem?

Answer

Explanation:

Step1: Identify the data points

For medium pizza, diameter $d_1 = 12$ inches and cost $C_1=$10.99$. For $\pi$-zilla pizza, diameter $d_2 = 24$ inches and cost $C_2=$25.99$.

Step2: Use the average - rate - of - change formula

The average rate of change formula is $\frac{\Delta C}{\Delta d}=\frac{C_2 - C_1}{d_2 - d_1}$. Substitute the values: $\frac{25.99 - 10.99}{24 - 12}=\frac{15}{12}=1.25$.

Answer:

A. $$0.79$ B. $$1.25$ C. $$1.49$ D. $$1.99$

Explanation for Part B:

The average rate of change of $$1.25$ means that, on average, for each additional inch in the diameter of the pizza when moving from a medium - sized pizza to a $\pi$-zilla pizza, the cost of the cheese pizza increases by $$1.25$.

Answer for Part B:

On average, the cost of the cheese pizza increases by $$1.25$ for each additional inch in diameter when moving from a medium pizza to a $\pi$-zilla pizza.