Adriana used the data from a scatterplot she found on the U.S. Census Bureau's website to determine a regression model showing the relationship between the population in the area where she lived and the number of years, x, after she was born. The result was an exponential growth equation of the form `y = x _(0)(1+r ) ^(x).` Which of the following does `x _(0)` most likely represent in the equation ?

Options

A. The population in the year that she was born
B. The rate of change of the population over time
C. The maximum population reached during her lifetime
D. The number of years after her birth when the population reached its maximum

Answer

A

Explanation

When an exponential equation is weritten in the from `y = x _(0)(1+r)^(x),` the value of `x _(0)` gives the y-intercept of the equation's graph. To answer this question, you need to think about what the y-intercept would represent in the context described.
Whenever time is involved in a rrelationship that is modeled by an equation or a graph, it is almost always the independent variable and therefore graphed on the x-axis. Therefore, for this questin, population would be graphed on the y-axis, so `x _(0)` most likely represents the population when the time elapsed ws zero, or in other words, in the year that Adriana was born, making (A) correct.