HELP ASAP I WILL MARK BRAINLEST
Internet Usage The number of hours people in the United States
spent using the Internet each year from 1998 to 2001 can be
modeled by the function f(x) 5 26.4x 1 54.4 where x is the number
of years since 1998.
a. Graph the function and identify its domain and range.
b. Find the number of hours that people spent on the Internet
in 2000. Explain how you found your answer.
c. When did people spend about 120 hours per year on the
Internet? Explain how you found your answer.
Answers
Answer:
Look in picture
Step-by-step explanation:
Functions can be represented on graph and as equation.
The domain and the range of the function are [0,3] and [54.4,133.6]The number of hours spent in 2000 is 107.2People spend about 120 hours per year in 2001The function is given as:
[tex]f(x) = 26.4x + 54.4[/tex]
(a) The graph, domain and range
See attachment for the graph of [tex]f(x) = 26.4x + 54.4[/tex]
The function represents years from 1998 to 2001.
This means that:
[tex]x = 0[/tex] in 1998 and [tex]x =3[/tex] in 2001
So, the domain is: [tex][0, 3][/tex]
From the graph;
[tex]x = 0 \to f(x) = 54.4[/tex]
[tex]x = 3 \to f(x) = 133.6[/tex]
So, the range is [tex][54.4,133.6][/tex]
(b) Number of hours spent in 2000
First, we calculate x.
[tex]x = 2000 - 1998[/tex]
[tex]x =2[/tex] i.e. 2 years since 1998
So, we have:
[tex]f(x) = 26.4x + 54.4[/tex]
[tex]f(2) =26.4 \times 2 + 54.4[/tex]
[tex]f(2) =107.2[/tex]
(c) When people starts to spend 120 hours.
We have:
[tex]f(x) = 26.4x + 54.4[/tex]
Substitute 120 for f(x)
[tex]120 = 26.4x + 54.4[/tex]
Collect like terms
[tex]26.4x = 120 - 54.4[/tex]
[tex]26.4x = 65.6[/tex]
Solve for x
[tex]x = \frac{65.6}{26.4}[/tex]
[tex]x = 2.48[/tex]
Round 2.48 to the smallest integer greater than 2.48
[tex]x = 3[/tex]
This represents the number of years, since 1998.
So, the actual year is:
[tex]Year =1998 + 3[/tex]
[tex]Year = 2001[/tex]
Hence, people spend about 120 hours per year in 2001
Read more about functions and graphs at:
https://brainly.com/question/18806107
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Answers
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