Question

the given bar graph shows the percentage of gross domestic product (gdp) in a state going toward health care from 2007 through 2010, with projections for 2014 and 2019. the data are modeled by the function f(x)=1.4lnx + 15.1, where f(x) is the percentage of gross domestic product going toward health care x years after 2006. use this information to solve parts a and b. a. use the function to determine the percentage of gross domestic product that went toward health care in 2009. does this underestimate or overestimate the percent displayed by the graph? by how much? determine the percentage of gross domestic product that went toward health care in 2009 using the given function. % (do not round until the final answer. then round to the nearest tenth as needed.)

Explanation:

Step1: Determine the value of x for 2009

Since x is the number of years after 2006, for 2009, $x = 2009 - 2006=3$.

Step2: Substitute x into the function

Substitute $x = 3$ into $f(x)=1.4\ln x + 15.1$. So $f(3)=1.4\ln3+15.1$.
We know that $\ln3\approx1.0986$. Then $f(3)=1.4\times1.0986 + 15.1$.
First, calculate $1.4\times1.0986 = 1.53804$.
Then $f(3)=1.53804+15.1 = 16.63804$.

Step3: Compare with the graph - value

From the graph, the percentage for 2009 is 16.9.
The difference is $16.9 - 16.63804=0.26196\approx0.3$. Since $16.63804<16.9$, it underestimates.

Answer:

16.6, underestimates, 0.3