Question

1. function p is defined so that its output p(t) is the number of people living in an apartment building t months after it was constructed.

a. explain the meaning of p(24) = 125 in this situation.
b. explain the meaning of p(0) = 0.
c. write a statement about function p that represents the fact that there were 212 people living in the apartment building 32 months after it was constructed.
d. explain the meaning of t in the equation p(t) = 400.
(from unit 5, lesson 3.)
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Explanation:

Part a

In the function \( P(t) \), \( t \) is the number of months after the apartment building was constructed, and \( P(t) \) is the number of people living there. So \( P(24) = 125 \) means 24 months (which is 2 years) after the apartment building was constructed, there are 125 people living in it.

For \( P(0) \), \( t = 0 \) represents the time when the apartment building was just constructed (0 months after construction). The value \( P(0)=0 \) means that at the time the building was constructed (0 months after), there were 0 people living in the apartment building.

We know that \( t = 32 \) months after construction, the number of people \( P(t) = 212 \). Using the function notation \( P(t) \) where \( t \) is the number of months and \( P(t) \) is the number of people, we can write \( P(32)=212 \) to represent that 32 months after the apartment building was constructed, there were 212 people living in it.

Answer:

24 months after the apartment building was constructed, there are 125 people living in it.

Part b