Question

in 2009, there were 7.6 million females enrolled in degree granting institutions of higher education; over the next several years, this number increased at a rate of 600,000 per year. a. model this situation by a linear equation (y = 0.6t + 7.6) b. estimate the number of females enrolled in 2018 (y = _____million) c. use this model to determine in what year 17.2 million females will be enrolled in degree granting institutions of higher education.

Answer 1

a) The model of the linear equation is:

$\begin{gathered} y=0.6t+7.6 \\ \text{Please note that 'y' is in millions} \end{gathered}$

b)

$\begin{gathered} \text{from 2009 to 2018 is 9years} \\ t=9 \\ \text{Substituing for t=9 in the modelled equation, we have:} \\ y=0.6(9)+7.6 \\ y=5.4+7.6 \\ y=13\text{ million} \end{gathered}$

c)

$\begin{gathered} y=0.6t+7.6 \\ 17.2=0.6t+7.6 \\ 17.2-7.6=0.6t \\ 9.6=0.6t \\ t=\frac{9.6}{0.6} \\ t=16 \\ \text{Adding 16years to the base year (2009), thus the final answer is 2025} \end{gathered}$