Answer:
(a)Food-12%
9b)Transportation-17%
Step-by-step explanation:
In the Year 2000
Therefore:
(a)Percentage of the average household income in 2000 was spent on food
(b)Percentage of the average household income in 2000 was spent on transportation
Due to length restrictions, we kindly invite to read the explanation of this question for further details on functions.
<h3>What are the characteristics of each of the three functions?</h3>
a) In this part we must evaluate each of the three functions at the given value of x:
Case 1
f(10) = 5 · 10 + 7
f(10) = 57
Case 2
f(10) = 10² + 6
f(10) = 106
Case 3
f(10) = 2¹⁰ + 3
f(10) = 1027
b) In this part we must evaluate each of the three functions at the given value of x:
Case 1
f(100) = 5 · 100 + 7
f(100) = 507
Case 2
f(100) = 100² + 6
f(100) = 10006
Case 3
f(100) = 2¹⁰⁰ + 3
f(100) = 1.267 × 10³⁰ + 3
c) In this part we must evaluate each of the three functions at the given value of x:
Case 1
f(1000) = 5 · 1000 + 7
f(1000) = 5007
Case 2
f(1000) = 1000² + 6
f(1000) = 1000006
Case 3
f(1000) = 2¹⁰⁰⁰ + 3
f(1000) = (1.268 × 10³⁰)¹⁰ + 3
f(1000) = 10.744 × 10³⁰⁰ + 3
f(1000) = 1.074 × 10³⁰¹ + 3
e) The <em>third</em> function increases the fastest.
f) In this part we need to compare the <em>third</em> function with respect to the <em>first</em> and <em>second</em> functions:
5 · x + 7 = 2ˣ + 3
2ˣ - 5 · x = 4
The solutions of the equation are x = - 0.675 and x = 4.81. The function will exceed the other <em>first</em> function at x = 4.81.
x² + 6 = 2ˣ + 3
2ˣ - x² = 3
The solution of the equation is x = 4.588. The function will exceed the other <em>second</em> function at x = 4.588.
g) Yes, <em>exponential</em> functions with bases greater than 1 will surpass <em>polynomic</em> function at any point x such that x > 0.
h) The domain represents the set of x-values of a function and the range represents the set of y-values of a function. Then, the domain and range of each function is:
Case 1
Domain - All <em>real</em> numbers.
Range - All <em>real</em> numbers
Case 2
Domain - All <em>real</em> numbers.
Range - [6, +∞)
Case 3
Domain - All <em>real</em> numbers.
Range - (3, +∞)
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Step-by-step explanation:
Take the first derivative
Set the derivative equal to 0.
or
For any number less than -1, the derivative function will have a Positve number thus a Positve slope for f(x).
For any number, between -1 and 1, the derivative slope will have a negative , thus a negative slope.
Since we are going to Positve to negative slope, we have a local max at x=-1
Plug in -1 for x into the original function
So the local max is 2 and occurs at x=-1,
For any number greater than 1, we have a Positve number for the derivative function we have a Positve slope.
Since we are going to decreasing to increasing, we have minimum at x=1,
Plug in 1 for x into original function
So the local min occurs at -2, at x=1
Step-by-step explanation:
Hey there!
The given slope is; 3. And passing through point (-7,8).
Now,
Using one point formula.
Put all values to find equation.
Simplify them to get answer.
Therefore the required equation is 3x-y+29=0.
<em><u>Hope it helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>