Answer
a) $ 42.95 $%, underestimate, by $0.05$%
b) $R=1∶ \frac{53+0.28n}{47-0.28n}$
c) $ 3$ women, accurately predicts projections shown by the graph.
Work Step by Step
a)
$M=-0.28n + 47$
$n = 2003 - 1989 = 14$, as the formula works for n years after 1989.
$M = -0.28(14) +47 = 42.95$%
Bar Graph result = 43%
Formula estimation = 42.95%
Therefore, the formula is an underestimation by $0.05$%
b)
$R = Man:Woman$
$= 47 - 0.28n : 53+0.28n$
$= 1: \frac{53+0.28n}{47-0.28n}$
c)
$n = 2014-1989=25$, 25 years after 1989
Using earlier defined formula,
$1 : \frac{0.28(25)+53}{47-0.28(25)}$
$= 1:1.5$, 1.5 women per 1 man
for 2 men, $1\times2 : 1.5 \times2$
$2:3$, so 3 women per 2 men
Projections shown by graph = 40 men to 60 women, $40:60$
which simplifies to $1:1.5$
which is the same as our formula based result $1:1.5$
therefore $R$ accurately predicts projections shown by the Graph.
