Question

A new fashion trend is catching on at a high school. Five students came to school after the

holidays wearing new Palioxis-brand sneakers, and 6 months later, 36 total students were


wearing Palioxis sneakers. In the equation y = 5(r'), y is the number of students wearing the


sneakers after timet in years. Find r, and write an equation to estimate the number of students


in Palioxis sneakers after t years.

Answer 1

The rate of growth r of the fashion trend at the high school is approximately 51.84. Therefore, the equation to estimate the number of students in Palioxis sneakers after t years is y = 5(51.84^t).

Step-by-step explanation:

The question relates to exponential growth and is about finding the rate of growth of a fashion trend at a high school where initially, five students wore Palioxis-brand sneakers and after half a year, the number grew to 36. If we use the given equation y = 5(r^t), where y is the number of students wearing the sneakers after time t in years, we can substitute the known values into the equation. Because 6 months is half a year, we have y = 36 and t = 0.5. The equation becomes 36 = 5(r^0.5), which allows us to solve for r by first dividing through by 5 to give 7.2 = r^0.5. By squaring both sides, we find r = 7.2^2, hence, r ≈ 51.84. Therefore, the equation to estimate the number of students wearing Palioxis sneakers after t years is y = 5(51.84^t).

Learn more about Exponential Growth