Question

the number of people y (in millions) carrying a drivers license from the years 2013 to 2020 can be estimated by the linear equation y = 2.3x + 150, where x is the number of years after 2010.
a. use this equation to complete the ordered pair (10, ).
b. write a sentence explaining the meaning of the ordered pair in part (a).
c. if this trend continues, predict the number of people with drivers licenses in 2026.
(10, ■)
(simplify your answer.)
a. complete the ordered pair.

Explanation:

Step1: Substitute \(x = 10\) into the equation \(y=2.3x + 150\)

$$y=2.3\times10+150$$

Step2: Calculate the product \(2.3\times10\)

$$2.3\times10 = 23$$

Step3: Calculate the sum \(23+150\)

$$23 + 150=173$$

Answer:

a. \((10,173)\)

b. The ordered pair \((10,173)\) means that 10 years after 2010 (i.e., in 2020), the number of people (in millions) carrying a driver's license is 173.

c. First, find \(x\) for 2026. Since \(x\) is the number of years after 2010, \(x = 2026 - 2010=16\).

Step1: Substitute \(x = 16\) into the equation \(y = 2.3x+150\)

$$y=2.3\times16+150$$

Step2: Calculate the product \(2.3\times16\)

$$2.3\times16=(2 + 0.3)\times16=2\times16+0.3\times16=32+4.8 = 36.8$$

Step3: Calculate the sum \(36.8+150\)

$$36.8+150 = 186.8$$