Which of the lines that appear in the graph would be parallel to a line with a slope of 3 and a y-intercept at (0, 3)?
2 answers:
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The equation for exponential decay is 
, where <em>a</em> is the initial amount, <em>b</em> = 1 + <em>r</em> (the growth rate as a decimal number) and <em>x</em> is the number of time periods (in this case, minutes). Substituting the information we have:
. To the nearest tenth of a gram, this would be 1.0 grams.
To express a function of the form 
in vertex form 
where (h,k) is the vertex of the parabola, we need to find the vertex first.
To find the vertex we are going to use the vertex formula:
, and 
will be the function evaluated at 
.
We can infer from our function that
and 
. So lets find :
Now that we have, we can evaluate the function at 1 to find :
We have the vertex (1,3) of our parabola, so we can use its vertex form:
We can conclude that the vertex for of our parabola is <span>f(x) = (x + 1)2 + 3.</span>
To find the vertex we are going to use the vertex formula:
We can infer from our function that
Now that we have
We have the vertex (1,3) of our parabola, so we can use its vertex form:
We can conclude that the vertex for of our parabola is <span>f(x) = (x + 1)2 + 3.</span>