Question

The U.S. Black population is inclusive of three demographic subgroups as indicated by the Pew Research Center. These include Single-race, non-Hispanic Black people, multiracial, non-Hispanic Black people, and Black Hispanic people. In 2000 there were 36.2 million individuals included in the U.S. Black population. In 2019, the number was 46.8 million individuals. (https://www.pewresearch.org/social-trends/fact-sheet/facts-about-the-us-black-population/)a. Create a linear equation that models the U.S. Black population growth since 2000. round to two decimal places. Use B for the output letter and t for the input letter.b. Using the created equation in part (a), calculate the expected U.S. Black population in 2030.

Answer 1

Let

t = number of years passed since 2000

B(t) = the number of Black population in millions.

We have two points given

(0,36.2) = year 2000, 36.2 million population

(19, 46.8) = year 2019, 46.8 million population

Part A: Linear equation that models U.S. Black population

Using the two points, determine the slope of the linear equation

$\begin{gathered} (t_1,y_1)=\left(0,36.2\right) \\ (t_2,y_2)=\left(19,46.8\right) \\ \\ m = \dfrac{46.8 - 36.2}{19 - 0} \\ m = \dfrac{10.6}{19} \\ m=0.557895 \\ \\ \text{Rounding to two decimal places, the slope is} \\ m=0.56 \end{gathered}$

The y-intercept is the value of the function when t = 0, the y-intercept therefore is b = 36.2.

Putting it together, the linear equation that models the US Black population growth in millions since 2000 is

$B(t)=0.56t+36.2$

Part B: Calculating the expected US Black population in 2030.

In 2030, t = 30. Substitute these to our model equation and we get

$\begin{gathered} B(t)=0.56t+36.2 \\ B(30)=0.56(30)+36.2 \\ B(30)=16.8+36.2 \\ B(30)=53 \end{gathered}$

Therefore, in 2030, the US is expected to have 53 million Black population.