Question

The total percent of individuals aged 16 to 24 enrolled in college as of October of each year who completed high school during the preceding 12 months is f(x)=66.925x0.044, where x is the number of years after 1999.Complete parts (a)-(c).

Answer 1

Given:

a)

$f(x)=66.925x^{0.044}$

Here, x is the number of years after 1999.

For the year 2002,

$\begin{gathered} 2002-1999=3 \\ So,\text{ x=3} \\ f(x)=66.925x^{0.044} \\ f(3)=66.925(3)^{0.044} \\ =70.240\text{ percent} \end{gathered}$

For the year 2009,

$\begin{gathered} 2009-1999=10 \\ So,\text{ x=10} \\ f(x)=66.925x^{0.044} \\ f(10)=66.925(10)^{0.044} \\ =74.061 \end{gathered}$

Answer:

The total percent in 2002 is 70.240 %

The total percent in 2009 is 74.061 %.

b) The graph of the function from 2002 to 2017 is, The

c) For f(x)=100,

$\begin{gathered} f(x)=66.925x^{0.044} \\ 100=66.925x^{0.044} \\ \frac{100}{66.925}=x^{0.044} \\ x^{0.044}=\frac{100}{66.925} \\ Note\colon0.044=\frac{11}{250}^{} \\ (x^{0.044}_{})^{\frac{250}{11}}=(\frac{100}{66.925})^{\frac{250}{11}} \\ x=(\frac{100}{66.925})^{\frac{250}{11}} \end{gathered}$

It implies that the value of x will exist for which the percentage will become 100.