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[Algebra 2 Quadratics] 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^t), y is the number of students wearing the
sneakers after time tin years. Find r, and write an equation to estimate the number of students
in Palioxis sneakers after t years.

Respuesta :

The exponential equation that estimates that number of students wearing Palioxis sneakers after t years is given by:

[tex]y = 5(7.2)^t[/tex]

What is an exponential function?

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

  • a is the initial value.
  • b is the rate of change.

In this problem, the function is:

[tex]y = 5r^t[/tex]

We have that when t = 0.5, as the time is measured in years, y = 36, hence we can use this to replace these numbers into the equation and find r:

[tex]5r^{0.5} = 36[/tex]

[tex]\sqrt{r} = \frac{36}{5}[/tex]

[tex]r = \left(\frac{36}{5}\right)[/tex]

r = 7.2.

Hence the equation that estimates that number of students wearing Palioxis sneakers after t years is given by:

[tex]y = 5(7.2)^t[/tex]

More can be learned about exponential functions at https://brainly.com/question/25537936

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