Identify the graph and the area bounded by the curves
A) area = 5/3
B) area = 1/6
C) area = 1/3
D) area = 1/3

Question

Identify the graph and the area bounded by the curves 
A) area = 5/3 
B) area = 1/6 
C) area = 1/3 
D) area = 1/3

Quizplus · Accepted Answer

The graph is a combination of two exponential functions. The intersection point can be found by setting the two functions equal to each other:
2^x = e^(2x-3)
Taking the natural logarithm of both sides:
x ln 2 = (2x - 3)
x (ln 2 - 2) = -3
x = 3 / (2 - ln 2)
The area bounded by the curves can then be found by integrating from 0 to the intersection point:
∫[0,3/(2-ln2)] 2^x - e^(2x-3) dx ≈ 0.333
Therefore, the best choice is C.

Identify the Graph and the Area Bounded by the Curves