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E Homework: 2.3 Linear Inequalities
Question 14, 2.3.101
Part 1 of 2
Assume that in 2005 consumers used credit and debit cards to pay for 43% of all purchases. This percentage is projected to be 58% in 2011.
(a) Find a linear function that models the data, where x is the year and P(x) is the percentage.
(b) Estimate when this percentage was between 48% and 53%.
(a) P(x) =
(Simplify your answer. Use integers or decimals for any numbers in the expression.)

Respuesta :

MrRoyal

Linear functions are functions that change at a constant rate

The linear function that models the data is [tex]P(x) = 0.025x -49.695[/tex]

The equation of the linear function

From the question, we have the following ordered pairs

(x,P(x)) = (2005,43%) and (2011,58%)

Start by calculating the slope (m)

[tex]m = \frac{P(x2) - P(x1)}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{58\% - 43\%}{2011 - 2005}[/tex]

Evaluate the differences

[tex]m = \frac{15\%}{6}[/tex]

Evaluate the quotient

[tex]m = 2.5\%[/tex]

The linear function is then calculated as:

[tex]P(x) = m(x - x_1)+ P(x_1)[/tex]

So, we have:

[tex]P(x) = 2.5\%(x - 2005) + 43\%[/tex]

Rewrite as:

[tex]P(x) = 0.025(x - 2005) + 0.43[/tex]

This gives

[tex]P(x) = 0.025x -50.125 + 0.43[/tex]

[tex]P(x) = 0.025x -49.695[/tex]

Hence, the linear function that models the data is [tex]P(x) = 0.025x -49.695[/tex]

Read more about linear functions at:

https://brainly.com/question/15602982

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