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{{ printedBook.courseTrack.name }} {{ printedBook.name }} This problem deals with the type of functions known as exponential functions, which are written in the form $y=a⋅b_{x}.$ Exponential functions describe percentage changes from an initial value $a$. The constant $a$ graphically specifies the vertical intercept, and $a$ is the growth factor or decay factor. We start with the two functions that have a vertical intercept at $y=3$.

The functions $B$ and $C$ has an intial value of of $3.$ $ By=3⋅1.1_{x}Cy=3⋅0.95_{x}. $ From the graph we can see that it corresponds to functions $g(x)$ and $k(x).$

We can see that one function increases and decreases. The one that increases must correspond to $y=3⋅1.1_{x}$ since it has a growth factor and the function $y=3⋅0.95_{x}$ corresponds to the one that decreases. $ g(x)−By=3⋅1.1_{x}k(x)−Cy=3⋅0.95_{x}. $

We have two graphs left, $f(x)$ and $h(x),$ and two function rules. $ Ay=6⋅1.01_{x}Dy=6⋅1.4_{x} $ We can see that the graphs are both growing but at different rates.

If we look at the growth factors, we see that $A$ only grows s by $1%$ for each step along the $x$-axis, while $D$ grows rapidly by an entire $40%$. Thus, we can make our final conclusions. $ h(x)−Ay=6⋅1.01_{x}g(x)−By=3⋅1.1_{x}k(x)−Cy=3⋅0.95_{x}f(x)−Dy=6⋅1.4_{x} $