Part A

The function [tex]\( f \)[/tex], where [tex]\( f(n) = 1,200n + 3,500 \)[/tex], represents the number of people in a town who owned a smartphone [tex]\( n \)[/tex] years after 2007.

How many people owned a smartphone in this town in the year 2010?

Enter a number in the box.
[tex]\[ \boxed{} \][/tex] people

Part B

Consider the function [tex]\( p \)[/tex], where [tex]\( p(x) \)[/tex] represents the percent of adults in the United States who owned a smartphone [tex]\( x \)[/tex] years after 2011.

What does [tex]\( p(5) = 68 \)[/tex] represent?

Select from the drop-down lists to complete the sentence correctly.

In the year [tex]\[ \boxed{} \][/tex]
[tex]\[ \boxed{} \][/tex] of the adults in the United States owned a smartphone.

Question

luis2030 luis2030

30-07-2024
Mathematics

Answered

Part A

The function [tex]\( f \)[/tex], where [tex]\( f(n) = 1,200n + 3,500 \)[/tex], represents the number of people in a town who owned a smartphone [tex]\( n \)[/tex] years after 2007.

How many people owned a smartphone in this town in the year 2010?

Enter a number in the box.
[tex]\[ \boxed{} \][/tex] people

Part B

Consider the function [tex]\( p \)[/tex], where [tex]\( p(x) \)[/tex] represents the percent of adults in the United States who owned a smartphone [tex]\( x \)[/tex] years after 2011.

What does [tex]\( p(5) = 68 \)[/tex] represent?

Select from the drop-down lists to complete the sentence correctly.

In the year [tex]\[ \boxed{} \][/tex]
[tex]\[ \boxed{} \][/tex] of the adults in the United States owned a smartphone.

Answer :

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Part A:

We are given the function [tex]\( f(n) = 1200n + 3500 \)[/tex], which represents the number of people in a town who owned a smartphone [tex]\( n \)[/tex] years after 2007.

To find the number of people who owned a smartphone in the year 2010, we need to determine [tex]\( n \)[/tex], the number of years after 2007.

Calculate [tex]\( n \)[/tex]:
[tex]\[ n = 2010 - 2007 = 3 \][/tex]

Substitute [tex]\( n = 3 \)[/tex] into the function [tex]\( f \)[/tex]:
[tex]\[ f(3) = 1200 \times 3 + 3500 \][/tex]

So, the number of people who owned a smartphone in 2010 is:
[tex]\[ \boxed{7100} \][/tex] people

Part B:

We are given the function [tex]\( p(x) \)[/tex], where [tex]\( p(x) \)[/tex] represents the percent of adults in the United States who owned a smartphone [tex]\( x \)[/tex] years after 2011.

The information [tex]\( p(5) = 68 \)[/tex] means that 68% of adults in the United States owned a smartphone [tex]\( x = 5 \)[/tex] years after 2011.

Calculate the year:
[tex]\[ \text{Year} = 2011 + 5 = 2016 \][/tex]

So, in the year [tex]\( \boxed{2016} \)[/tex], [tex]\( \boxed{68}\%\)[/tex] of the adults in the United States owned a smartphone.