Question

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1. the total number of views for video a after t days can be modeled by the equation v = 12t. the total number of views for video b after t days is shown by the graph. describe how the rates of change for the two functions are different.

Explanation:

Step1: Identify Video A's rate

The function for Video A is $v=12t$, which is linear. For linear functions $y=mx+b$, the rate of change is the slope $m$. Here, the rate of change is a constant $12$ views per day.

Step2: Analyze Video B's rate

The graph for Video B is a curve (exponential-like). Calculate the rate of change between consecutive days:

• Days 0-1: $\frac{0-0}{1-0}=0$ (or from 0 to ~4, rate ≈4)
• Days 1-2: $\frac{12-4}{2-1}=8$
• Days 2-3: $\frac{24-12}{3-2}=12$
• Days 3-4: $\frac{48-24}{4-3}=24$
• Days 4-5: $\frac{84-48}{5-4}=36$

The rate of change increases as $t$ increases, so it is not constant.

Step3: Compare the two rates

Video A has a constant rate, while Video B's rate grows over time.

Answer:

The rate of change for Video A is a constant 12 views per day (linear function), while the rate of change for Video B increases as the number of days passes (non-linear, increasing rate).