Answer:
D
Step-by-step explanation:
I see the curve given crosses the point (1,3).
So let's check and see which of the given equations is satisfied by that point.
Checking choice A:
[tex]y=2(\frac{1}{4})^x[/tex] with (x,y)=(1,3):
[tex]3=2(\frac{1}{4})^1[/tex]
[tex]3=2(\frac{1}{4})[/tex]
[tex]3=\frac{1}{2}[/tex]
So choice A is not right.
Checking choice B:
[tex]y=2(\frac{1}{2})^x[/tex] with (x,y)=(1,3):
[tex]3=2(\frac{1}{2})^1[/tex]
[tex]3=2(\frac{1}{2})[/tex]
[tex]3=1[/tex]
So choice B is not right.
Checking choice C:
[tex]y=6(\frac{1}{4})^x[/tex] with (x,y)=(1,3):
[tex]3=6(\frac{1}{4})^1[/tex]
[tex]3=6(\frac{1}{4})[/tex]
[tex]3=\frac{3}{2}[/tex]
So choice C is not right.
Checking choice D:
[tex]y=6(\frac{1}{2})^x[/tex] with (x,y)=(1,3):
[tex]3=6(\frac{1}{2})^1[/tex]
[tex]3=6(\frac{1}{2})[/tex]
[tex]3=3[/tex]
So choice D is the only choice that would contain the point (1,3) when graphed.
So choice C is not right.
Answer:
D
Step-by-step explanation:
The standard form of an exponential function is
y = a [tex]b^{x}[/tex]
Using points from the graph to find a and b
Using (0, 6 ), then
6 = a [tex]b^{0}[/tex] = a × 1 ⇒ a = 6
Using (1, 3 ), then
3 = 6 [tex]b^{1}[/tex] ⇒ b = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
The exponential function is
f(x) = 6 [tex](\frac{1}{2}) ^{x}[/tex] → D
