How do you graph y=1.1(3)^x?

1 Answer
May 14, 2018

See explanation

Explanation:

Given: 1.1(3)^x

Just because I prefer it this way write as y=11/10xx3^x

color(blue)("Determine the "y_("intercept"))

The y_("intercept") occurs at x=0

However, 3^0=1 giving

color(brown)(y_("intercept")=11/10xx1 = 11/10)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Consider the case "x<0)

This changes 3^x into some root of 3

So as x becomes increasingly negative 3^x becomes less and less. So as x tends to negative infinity then:

color(brown)(y=11/10xxlim_(x->oo^(-))(3^x)color(white)("ddd") ->color(white)("ddd")y=11/10xx0=0)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Consider the case "x>0)

As x becomes increasingly greater the 3^x increases exponentially.

color(brown)(y=11/10xxlim_(x->oo^(+))(3^x)color(white)("ddd") ->color(white)("ddd") y=11/10xxoo = oo

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