David concludes that 7x^2will always output larger values than 2^x for the same value of x. Do you agree? Explain your reasoning.

False. One counter example is when x = 10.

When x = 10, we have

7x^2 = 7*10^2 = 7*100 = 700

2^x = 2^100 = 1.27 * 10^30

The result of 2^x is much larger than 700. The result is so large that we must use scientific notation to be able to fit it on the page. We could write out all the digits, but we would need 30 or more digits.

As a visual to see that 2^x will be larger at some point, I recommend graphing y = 7x^2 and y = 2^x together on the same xy grid. See the graph below. The two curves intersect at point A, which is roughly when x = 9.22; anything beyond this x value will have 2^x be larger than 7x^2.

6.45 feet

Step-by-step explanation:

He starts 17 and 1/2 feet off the ground

Elevation relative to ground: 17 1/2

Then he increases the height by 4 and 3/4

Expression: 17 1/2 +4 3/4

Elevation relative to ground: 22 1/4

Next he decreases the elevation by 15.8 feet

Expression: 22.25-15.8

Elevation relative to ground: 6.45

The answer 6.45 feet from the ground