A study in a small town showed that the percent of residents who have college degrees can be modeled by the function $\mathrm { P } = 37 \mathrm { x } ^ { 0.33 }$ where x is the number of years since 2005. Does this model indicate that the percent of
Residents with a college degree is increasing or decreasing?
A) Increasing
B) Decreasing

Question

Quizplus · Accepted Answer

The exponent $0.33$ in the function $P = 37x^{0.33}$ indicates that as $x$ (years since 2005) increases, $P$ (percent of residents with college degrees) also increases, albeit at a decreasing rate. This is because any positive exponent greater than 0 but less than 1 applied to an increasing $x$ will result in an overall increase in $P$, thus indicating an increasing trend in the percentage of residents with college degrees.

A Study in a Small Town Showed That the Percent P=37x0.33\mathrm { P } = 37 \mathrm { x } ^ { 0.33 }P=37x0.33

A Study in a Small Town Showed That the Percent $\mathrm { P } = 37 \mathrm { x } ^ { 0.33 }$