Question

Let d(t) be the number of dogs in the united States in year t, and let c(t) be the number of cats in the United States in year t, where t=0 corresponds to 2000.

(a.) Find the function p(t) that represents the total number of dogs and cats in the United States.


(b.) Interpret the value of p(5).

(c.) Let n(t) represent the population of the United States in year t, where t=0 corresponds to 2000. Find and interpret h(t) = p(t) / n(t).

Answer 1

Answer with Step-by-step explanation:

Since we have given that

d(t) is the number of dogs,

c(t) is the number of cats.

(a.) Find the function p(t) that represents the total number of dogs and cats in the United States.

P(t) is the total number of dogs and cats.

So, it becomes,

`p(t)=d(t)+c(t)`

(b.) Interpret the value of p(5).

p(5) = d(5)+c(5)

Since, t=0 corresponds to 2000.

So, t=5 corresponds to 2005.

So, p(5) is the total number of dogs and cats in 2005.

(c.) Let n(t) represent the population of the United States in year t, where t=0 corresponds to 2000. Find and interpret h(t) = p(t) / n(t).

`h(t)=(p)t))/(n(t))\\\\h(t)=(d(t)+c(t))/(n(t))`