The population $P$ of a certain city $y$ years after the last census is modeled by the equation below, where $r$ is a constant and $P_{y}$ is the population when $y=0$.<br/><br/>$P=P_{0}(1+r)^{y}$<br/><br/>If during this time the population of the city decreases by a fixed percent each year, which of the following must be true?

MM

Mashaal Masha

Feb 20, 2024

The population $P$ of a certain city $y$ years after the last census is modeled by the equation below, where $r$ is a constant and $P_{0}$ is the population when $y=0$.$P=P_{0}(1+r)^{y}$If during this time the population of the city decreases by a fixed percent each year, which of the following must be true?

Difficulty: Hard

A:

$r<-1$

B:

$-1<r<0$

C:

$0<r<1$

D:

$r>1$

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ID: 65d4eda1dbc6daab1c0235f4