 # A "Student Drug Use and Health Survey" of Ontario high school students found that the percentage of students that reported serious psychosocial distre Khaleesi Herbert 2021-02-08 Answered
A "Student Drug Use and Health Survey" of Ontario high school students found that the percentage of students that reported serious psychosocial distress in the past month increased from 10.7% in 2013 to 17.1% in 2017.
Assuming a standard exponential growth trend, what is the annual growth rate in the percentage of students reporting serious psychosocial distress in the past month?
You can still ask an expert for help

## Want to know more about Exponential growth and decay?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it rogreenhoxa8

Let t=0 for 2013, t=1 for 2014, t=2 for 2015, t=3 for 2016, t=4 for 2017.
Assuming the exponential growth rate as,
$y\left(t\right)=axxekt$ where y is the % of students having serious psychosocial distress at time ta is value at starting t=0k is the rate of growtht is time
Therefore, at t=4, y=17.1
Thus,
$17.1=10.7\cdot {e}^{k\cdot 4}$
${e}^{4k}=lo{g}_{e}\left(\frac{17.1}{10.7}\right)=0.4688$
k=0.1172
Hence, the equation of exponential growth rate is
$y\left(t\right)10.7\ast {e}^{0.1172t}$
Thus the annual growth rate is calculated at t=1 we get
$y\left(1\right)=10.7\cdot {e}^{0.1172\ast 1}$
$y\left(1\right)=10.7\ast {e}^{0.1172}$
y(1)=12.03
Hence, the annual growth rate in the percentage of students reporting serious psychosocial distress in the past month is 12.03%.