SOLUTION: At what point will f(x) = 3^x exceed g(x) = 2x + 5 and h(x) = x^2 +4? A. (x,y) = (1,7) B. (x,y) = (2.4, 9.8) C. (x,y) = (1.8, 3.7) D. (x,y) = (2,9)

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: At what point will f(x) = 3^x exceed g(x) = 2x + 5 and h(x) = x^2 +4? A. (x,y) = (1,7) B. (x,y) = (2.4, 9.8) C. (x,y) = (1.8, 3.7) D. (x,y) = (2,9)      Log On


   

Question 1202280: At what point will f(x) = 3^x exceed g(x) = 2x + 5 and h(x) = x^2 +4?
A. (x,y) = (1,7)
B. (x,y) = (2.4, 9.8)
C. (x,y) = (1.8, 3.7)
D. (x,y) = (2,9)
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

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



Graph comparing f(x) in green and h(x) in blue



All three graphs together

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.