2015 Countdown Problem #22: The Curve

Geometry Level 1

The image shows a part of a graph. Below are four equations:

I : y = 2015 e x y=\frac{2015}{e^x}

II : y = 2015 e x y=2015{e}^x

III : y = 2015 x y={2015}^x

IV : y = e 2015 x y=e^{2015x}

Which equation(s), when plotted, will produce the graph above?

This problem is part of the set 2015 Countdown Problems .


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2 solutions

By letting the value of x=0, the value of y must be equal to 1, and only III and IV satisfy these condition..

Highry Tan
Dec 26, 2014

Check if (0,1) is a solution to each equation. III and IV satisfy. Since the graph is going upward, the variable in the exponential equation must be positive. Since III and IV satisfy both conditions, III and IV are the answers.

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