Question

the graphs, on the right, show the percentage of jobs in a countrys labor force held by men and women from 1970 through 2015. the formula p = 1.8√t + 38 models the percentage of jobs in the labor force, p, held by women t years after 1970. answer parts a through c. p = 49% (round to the nearest whole number as needed.) b. use the mathematical model to determine the percentage of jobs in the labor force held by women in 2010. p = 49.4% (round to the nearest tenth as needed.) c. according to the formula, when will 60% of jobs in the labor force be held by women? 60% of jobs in the labor force will be held by women by (round to the nearest whole number as needed.)

Explanation:

Step1: Set up the equation

We are given the formula $p = 1.8\sqrt{t}+38$ and we want to find $t$ when $p = 60$. So we set up the equation $60=1.8\sqrt{t}+38$.

Step2: Isolate the square - root term

Subtract 38 from both sides of the equation: $60 - 38=1.8\sqrt{t}$, which simplifies to $22 = 1.8\sqrt{t}$.

Step3: Solve for $\sqrt{t}$

Divide both sides of the equation by 1.8: $\sqrt{t}=\frac{22}{1.8}=\frac{220}{18}=\frac{110}{9}\approx12.22$.

Step4: Solve for $t$

Square both sides of the equation: $t = (\frac{110}{9})^2=\frac{12100}{81}\approx149.38$.

Step5: Find the year

Since $t$ is the number of years after 1970, the year is $1970 + 149=2119$.

Answer:

2119