Subjects algebra

Exponential Linear 90D692

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1. The problem asks to graphically represent the functions $f(x) = e^x$ and $f(x) = 2x + 4$ and find the coordinates of their intersection if the second function is a straight line. 2. The function $f(x) = e^x$ is an exponential function, and $f(x) = 2x + 4$ is a linear function (a straight line). 3. To find the intersection points, set the two functions equal: $$e^x = 2x + 4$$ 4. This equation cannot be solved algebraically with elementary functions, so we use numerical methods or graphing to approximate the solution. 5. By graphing, we observe the intersection point approximately near $x = 1.256$. 6. Substitute $x = 1.256$ into $f(x) = 2x + 4$ to find the $y$-coordinate: $$y = 2(1.256) + 4 = 2.512 + 4 = 6.512$$ 7. Therefore, the coordinates of the intersection point are approximately $(1.256, 6.512)$. This completes the solution.