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)=1.5lnx + 14.5, 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 2008. 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 2008 using the given function.

15.5% (do not round until the final answer. then round to the nearest tenth as needed.)

does this underestimate or overestimate the percent displayed by the graph? select the correct choice below and fill in the answer box to complete your choice.

○ a. underestimates by □%

○ b. overestimates by □%

Explanation:

Step1: Calculate \(x\) for 2008

Since \(x\) is the number of years after 2006, for 2008, \(x = 2008 - 2006=2\).

Step2: Substitute \(x = 2\) into the function \(f(x)=1.5\ln x + 14.5\)

$$
LATEXBLOCK0
$$

Step3: Compare with the graph value

From the graph, the value for 2008 is \(15.2\).
Calculate the difference: \(15.5 - 15.2=0.3\)

Answer:

A. Underestimates by \(0.3\%\)