Question

Part B: the model when will 18.1% of gross to medics product to go to forward health care round to the nearest year

Answer 1

a.

Since x represents the number of years after 2006, we need to use x = 3 to calculate the gross domestic product in 2009:

`\begin{gathered} f(x)=1.2\ln x+14.9\\ \\ f(3)=1.2\ln3+14.9\\ \\ f(3)=1.2\cdot1.0986+14.9\\ \\ f(3)=16.2 \end{gathered}`

So the GDP in 2009 is 16.2%.

Looking at the graph, the value for 2009 is 16.5.

Therefore the function underestimates the percent displayed by the graph by 0.3.

b.

To find the year when the GDP will be 18.1%, we can use f(x) = 18.1 and then calculate the value of x:

`\begin{gathered} 18.1=1.2\ln x+14.9\\ \\ 1.2\ln x=18.1-14.9\\ \\ 1.2\ln x=3.2\\ \\ \ln x=(3.2)/(1.2)\\ \\ \ln x=2.667\\ \\ x=e^(2.667)\\ \\ x=14.4 \end{gathered}`

Rounding to the nearest year, we have x = 14, therefore the year will be 2020.