e^(3-2x) = 4
How do I solve this graphically? Thanks.
Make a graph of e^(3 - 2x) vs x for various values of x from 0 to 2. The answer will be in that interval. Where the graph crosses f(x) = y = 4, read off the value of x. That will be the answer.
When x = 0, e^(3-2x)= e^3 = 20.09
When x = 0.5, e^(3-2x) = e^2 = 7.389
When x = 1, e^(3-2x)= e = 2.718
The answer f(x) = 4, will be between x = 0.5 and 1. Try x=0.8! It's pretty close to the right answer.
To solve the equation e^(3-2x) = 4 graphically, you can plot the function e^(3-2x) on a graph, along with a horizontal line y=4.
Start by selecting various values of x within the desired interval, for example, x=0, x=0.5, and x=1. Calculate the corresponding values of e^(3-2x) for each x value.
When x=0, e^(3-2x) = e^3 ≈ 20.09.
When x=0.5, e^(3-2x) = e^2 ≈ 7.389.
When x=1, e^(3-2x) = e ≈ 2.718.
Now, plot these points on a graph with x on the x-axis and e^(3-2x) on the y-axis. In addition, draw a horizontal line at y=4.
Look for the points where the graph of e^(3-2x) intersects the line y=4. These points represent values of x where the equation is satisfied.
Based on the plotted points, it appears that the solution lies between x=0.5 and x=1. Try picking a value within this range, for example, x=0.8, and check the corresponding value of e^(3-2x).
By evaluating e^(3-2x) at x=0.8, you should find that it's pretty close to 4, indicating that x=0.8 is approximately the solution to the equation e^(3-2x) = 4.