The estimated number of Amazon Prime members in millions, P,...

The estimated number of Amazon Prime members in millions, $P,$ in the United States $q$ quarters since March 2015 can be represented by the equation $$ P=7.89 q+33.73 . $$ a. Find the estimated number of Amazon Prime members in the U.S. in March of 2017. (March 2017 is 8 quarters, 2 years, since March $2015 .$ b. Find the estimated number of Amazon Prime members in the U.S. in March of 2020 c. In what quarter will the estimated number of Amazon Prime members in the U.S. be 133 million?

The estimated number of Amazon Prime members
in millions, $P,$ in the United States $q$ quarters since March 2015 can be represented by the equation
$$
P=7.89 q+33.73 .
$$
a. Find the estimated number of Amazon Prime members in the U.S. in March of 2017. (March 2017 is 8 quarters, 2 years, since March $2015 .$
b. Find the estimated number of Amazon Prime members in the U.S. in March of 2020
c. In what quarter will the estimated number of Amazon Prime members in the U.S. be 133 million?

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Key Concepts

Solving Linear Equations

Solving linear equations involves isolating the unknown variable through algebraic manipulation. This process is important when determining at what point, such as a specific time period, a modeled quantity reaches a given value.

Linear Functions

A linear function is a mathematical model that describes a relationship between two variables with a constant rate of change, typically expressed in the form y = mx + b. It is used to model situations where one quantity increases or decreases at a steady rate over time.

Slope

The slope, represented by m in the equation y = mx + b, describes the rate at which the dependent variable changes relative to the independent variable. It quantifies how fast or slow a quantity is growing or declining over a given interval.

Y-intercept

The y-intercept, represented by b in the equation y = mx + b, indicates the starting value of the dependent variable when the independent variable is zero. It is crucial for understanding the initial condition of a system or model.

Substitution

Substitution involves replacing the variable in an equation with a specific value to evaluate the function at that point. This method is essential in applying mathematical models to obtain specific predictions or estimates.

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