Question

the graphs, on the right, show the percentage of jobs in a country’s labor force held by men and women from 1970 through 2015.
the formula ( p = 1.3sqrt{t} + 39 ) models the percentage of jobs in the labor force, ( p ), held by women ( t ) years after 1970. answer parts a through c.

a. use the appropriate graph to estimate the percentage of jobs in the labor force held by women in 2010.
( p = 47 % )
(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 = square % )
(round to the nearest tenth as needed.)

Explanation:

Step1: Determine the value of t

2010 is 2010 - 1970 = 40 years after 1970, so \( t = 40 \).

Step2: Substitute t into the formula

The formula is \( p = 1.3\sqrt{t} + 39 \). Substitute \( t = 40 \) into it:
\( p = 1.3\sqrt{40} + 39 \)
First, calculate \( \sqrt{40} \approx 6.3246 \)
Then, \( 1.3\times6.3246 \approx 8.222 \)
Finally, \( p \approx 8.222 + 39 = 47.222 \)

Step3: Round to the nearest tenth

Rounding 47.222 to the nearest tenth gives 47.2.

Answer:

47.2