Two different businesses model their profits over 15 years, where x is the year, f(x) is the profits of a garden shop, and g(x) is the profits of a construction materials business. Use the data to determine which function is exponential, and use the table to justify your answer. x f(x) g(x) 1995 $69,682.50 $72,429.27 2000 $78,943.50 $79,967.77 2005 $88,204.50 $88,290.88 2006 $90,056.70 $90,056.70 2007 $91,908.90 $91,857.83 2010 $97,465.50 $97,480.27 f(x) is exponential; an exponential function increases more slowly than a linear function. f(x) is exponential; f(x) increased more overall than g(x). g(x) is exponential; g(x) has a higher starting value and higher ending value. g(x) is exponential; an exponential function increases faster than a linear function.

Respuesta :

Answer:

its g(x) is exponential; an exponential function increases faster than a linear function. I got it right.

Step-by-step explanation:

There are several functions that can be used to model different situations.

g(x) represents an exponential function

An exponential function is represented as:

[tex]\mathbf{y = ab^x}[/tex]

For g(x)

Represent the years from 1995 with x.

  • When year = 1995, x =0 and y = 72429.27
  • When year = 2000, x =5 and y = 79967.77

So, we have:

[tex]\mathbf{y = ab^x}[/tex]

[tex]\mathbf{ab^0 = 72429.27}[/tex]

[tex]\mathbf{a = 72429.27}[/tex]

[tex]\mathbf{y = ab^x}[/tex]

[tex]\mathbf{ab^5 = 79967.77}[/tex]

Substitute [tex]\mathbf{a = 72429.27}[/tex]

[tex]\mathbf{72429.27b^5 = 79967.77}[/tex]

Divide both sides by 72429.27

[tex]\mathbf{b^5 = 1.1041}[/tex]

Take 5th root of both sides

[tex]\mathbf{b = 1.02}[/tex]

So, the function is:

[tex]\mathbf{g(x) = 72429.27(1.02)^x}[/tex]

In 2005, when x = 10, we have:

[tex]\mathbf{g(10) = 72429.27(1.02)^{10} = 88290.88}[/tex]

In 2006, when x = 11, we have:

[tex]\mathbf{g(10) = 72429.27(1.02)^{11} = 90056.70}[/tex]

And so on.

Hence,  g(x) is exponential; an exponential function increases faster than a linear function.

Read more about exponential functions at:

https://brainly.com/question/13545998

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