written assignment module 4

If 𝑓(𝑝) = 50 what can you say about 𝑝?

p=125

What is the average rate of change between 𝑝 = 0 and 𝑝 = 150? What would the units be for average rate of change in the context of this problem?

-5/3 thousands tree/thousands people

Is the number of trees a function of 𝑝? How do you know?

Yes because for each value of p, there is exactly one corresponding value of the number of trees. And the graph passes the vertical line test.

Let 𝑡 = 𝑓(𝑝) where 𝑡 is the number of trees in thousands. What is 𝑓(75)? What does it mean in the context to this problem?

It means there were 200 thousand trees when there were 75 thousand people

Let 𝑡 = 𝑓(𝑝) where 𝑡 is the number of trees in thousands. In words, what is the input of 𝑓?

The input of f is p (the number of people in thousands)

Let 𝑡 = 𝑓(𝑝) where 𝑡 is the number of trees in thousands. In words, what is the output of 𝑓?

The output of f is t (the number of trees in thousands)

What is the 𝑝-intercept(s) and what does it mean in the context of this problem?

The p-int is 150 because that is where t=0

What is the 𝑡-intercept(s) and what does it mean in the context of this problem?

The t-int is 250 because that is where p=0

Let 𝑡 = 𝑓(𝑝) where 𝑡 is the number of trees in thousands. What is the domain of 𝑓 (in interval notation)?

[0, 175]

Let 𝑡 = 𝑓(𝑝) where 𝑡 is the number of trees in thousands. What is the range of 𝑓 (in interval notation)?

[0, 300]