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Hitman42 [59]
2 years ago
5

Select the correct answer from each drop-down menu. observe the functions below. complete the following sentences to compare the

two functions. over the interval , the average rate of change of g is greater than the average rate of change of f. as the value of x increases, the average rates of change of f and g , respectively. when the value of x is equal to 8, the value of . it can be further generalized that a quantity increasing exponentially will exceed a quantity increasing linearly.
Mathematics
1 answer:
MrRissso [65]2 years ago
7 0

The answers will be:

  1. (4, 5)
  2. remain constant and increase
  3. g(x) exceeds the value of f(x)

<h3>What is Slope and curve?</h3>

a) The slope of the curve g(x) roughly matches that of f(x) at about x=4. Above that point, the curve g(x) is steeper than f(x), so its average rate of change will exceed that of f(x). An appropriate choice of interval is (4, 5).

b) As x increases, the slope of f(x) remains constant (equal to 4). The slope of g(x) keeps increasing as x increases. An appropriate choice of rate of change descriptors is (remain constant and increase).

c) The curves are not shown in the problem statement for x = 8. The graph below shows that g(x) has already exceeded f(x) by x=7. It remains higher than f(x) for all values of x more than that. We can also evaluate the functions to see which is greater:

 f(8) = 4·8 +3 = 35

 g(8) = (5/3)^8 ≈ 59.54 . . . . this is greater than 35

 g(8) > f(8)

d) Realizing that an exponential function with a base greater than 1 will have increasing slope throughout its domain, it seems reasonable to speculate that it will always eventually exceed any linear function (or any polynomial function, for that matter).

To know more about Slope follow

brainly.com/question/3493733

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Problem 9
lapo4ka [179]

Answer:

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Step-by-step explanation:

Leon starts at 12PM with 12 gallons of gas, and after 2 hours he has used 5 gallons of gas. This means that every 2 hours he uses 5 gallons of gas.

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This is a simple proportion, and now we know he uses 2.5 gallons of gas per hour.

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The 7-3 is because Leon doesn't stop when his tank is empty, he stops 3 gallons earlier. We are dividing by 2.5 because that is how much gas he uses per hour, meaning the result of this division (1.6) is how many hours he has left.

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Given :

0.00467

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0.00467=\frac{0.00467}{100000}

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