Solved on Feb 02, 2024

Determine the dependent and independent variables in the population function P(y)=0.015y22.105y+278.090P(y)=0.015 y^{2}-2.105 y+278.090.

STEP 1

Assumptions
1. The function P(y)=0.015y22.105y+278.090P(y) = 0.015y^2 - 2.105y + 278.090 represents a relationship between the population in millions and age in years.
2. The population is denoted by PP.
3. The age is denoted by yy.
4. The population depends on the age.

STEP 2

Identify the dependent and independent variables.
In a function, the dependent variable is the one that depends on the value of another variable, which is known as the independent variable. The standard form of a function is f(x)f(x), where ff is the dependent variable and xx is the independent variable.

STEP 3

Apply this understanding to the given function P(y)P(y).
Here, PP represents the population and is written as a function of yy, which represents age. This means that the population depends on the age.

STEP 4

Conclude which variable is dependent and which is independent.
Since the population PP depends on the age yy, PP is the dependent variable and yy is the independent variable.
The dependent variable is PP and the independent variable is yy.

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