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Numerade Educator

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Problem 28 Hard Difficulty

Use a graph to estimate the values of $ x $ such that $ e^x > 1,000,000,000 $.

Answer

$x>20.723$

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Video Transcript

All right. So for this problem, we want to find out when the graph of y equals e to the X surpasses one billion so we can go ahead and type y equals e to the X into the calculator. And then we also want to put a horizontal lying at a height of one billion and one billion would be 10 to the ninth power, since there are nine zeros. So for a window, I've decided to go with negative 10 to 50 on my X axis, a negative 10 to 10 billion on my Y axis, making sure that I surpass one billion. And those numbers air flexible. You can try different things and find something that you like. Okay, so here's the graph of y equals e to the X, and the horizontal line is the graph of, um y equals one billion. So let's find the point of your section so we can go into the calculate menu, choose number five intersect and put the cursor on the first curve. Press enter, put the cursor on the second curve, press enter, and then put the cursor close to the intersection. Point and press enter and we see that at X equals 20.7. If we round to the nearest 10th we have X equals 20.7. That's when the value is one billion. So when X is greater than that number, either the ex will exceed one billion.