Answer
a. $ 17.0\%$,
underestimates the percent displayed by the graph by $0.3\%.$
b. in 2019
Work Step by Step
$\mathrm{a}$.
2009 = 2006 +3, so x=3.
$f(x)=1.2\ln x+15.7$
$ f(3)=1.2\ln 3+15.7\approx$17.0183347464$\approx 17.0$
According to the function, $ 17.0\%$ of GDP in 2009 went toward health care.
This underestimates the percent displayed by the graph by $0.3\%.$
$\mathrm{b}$.
When will $f(x)=18.5?$ (Insert and solve for x)
$18.5=1.2\ln x+15.7\qquad/-15.7$
$2.8=1.2\ln x\qquad/1.2$
$\displaystyle \frac{2.8}{1.2}=\ln x\qquad$... apply $e^{(...)}$ to both sides
... $\displaystyle \frac{2.8}{1.2}==\frac{28}{12}=\frac{7}{3}$ ...
$ x=e^{7/3}\approx$10.3122585013$\approx$10 years after 2009.
(in the year 2019)
