Question

The graph shows the functions f(x)=50e^0.1x and g(x)=200e^0.02x. At which x-value do the two curves appear to intersect? A. Around x=22.1. B. Around x=17.3. C. Around x=10.5. D. Around x=5.0.

Answer 1

Set 50 e^{0.1x} = 200 e^{0.02x}. Divide by 50: e^{0.1x} = 4 e^{0.02x}. Take ln: 0.1x = ln4 + 0.02x, so 0.08x = ln4. Thus x = ln4 / 0.08 ≈ 17.33.

Answer: B (around x = 17.3).