Answer:
the graph corresponds to function "D" [tex]f(x)=3\,(\frac{1}{5} )^x[/tex]
Step-by-step explanation:
Since the graph shown corresponds to an exponential "decay" (the function decreases as we move from left to right), the base of the exponent has to be a number smaller than 1 (one). So we examine the only two options that give such (options C and D which have fractions as the base - 1/3 and 1/5 respectively)
From there, we analyze which of the two functions satisfies the crossing of the y-axis at (0,3) which is clearly shown in the graph:
We study both:
function C at x = 0 gives:
[tex]f(x)= 5\,(\frac{1}{3})^x\\f(0)=5\,(\frac{1}{3})^0 \\f(0)=5\,(1)\\f(0)=5[/tex]
while function D at x = 0 gives:
[tex]f(x)= 3\,(\frac{1}{5})^x\\f(0)=3\,(\frac{1}{5})^0 \\f(0)=3\,(1)\\f(0)=3[/tex]
Therefore, the graph corresponds to function "D"
A correct option is an option (d)
From the given graph the function is increasing, therefore the base of the exponent must be greater than 1
And the best suited is the first, as it passes through the point,
y = 3
If you substitute x = 0 in the function result you have to give,
y = 3 and intersect the y-axis at that point
So, the required function is [tex]f(x)=3\times (\frac{1}{5} )^x[/tex]
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