Question 1202280
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Answer: Choice D
(x,y) = (2,9)



Reason:
Use a graphing calculator to find the approximate solution to 3^x = x^2+4 is x = 1.8
Then 3^x = 3^(1.8) = 7.2 approximately
F(x) exceeds h(x) at the point (1.8,7.2)


Use a graphing calculator to solve 3^x = 2x+5 and you should get x = 2 exactly
3^x = 3^2 = 9
2x+5 = 2*2+5 = 9
f(x) exceeds g(x) at (2,9)


Graph comparing f(x) in green and g(x) in blue
{{{
drawing(400,400,-2,4,-2,11,
graph(400,400,-2,4,-2,11,-100,3^x,2x+5),
circle(2,9,0.04),
circle(2,9,0.06),
circle(2,9,0.08),
locate(2-0.8,9+0.5,"(2,9)")
)
}}}



Graph comparing f(x) in green and h(x) in blue
{{{
drawing(400,400,-2,4,-2,11,
graph(400,400,-2,4,-2,11,-100,3^x,x^2+4),
circle(2,9,0.04),
circle(2,9,0.06),
circle(2,9,0.08),

circle(1.8,7.2,0.04),
circle(1.8,7.2,0.06),
circle(1.8,7.2,0.08),

locate(2-0.8,9+0.5,"(2,9)"),
locate(1.8+0.1,7.2-0.1,"(1.8,7.2)")
)
}}}



All three graphs together
{{{
drawing(400,400,-2,4,-2,11,
graph(400,400,-2,4,-2,11,-100,3^x,2x+5,x^2+4),
circle(2,9,0.04),
circle(2,9,0.06),
circle(2,9,0.08),
locate(2-0.8,9+0.5,"(2,9)")
)
}}}
f(x) = 3^x in green
g(x) = 2x+5 in blue (straight line)
h(x) = x^2+4 in purple (parabola)


Desmos and GeoGebra are two graphing apps I recommend.
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