Question

to determine the percentage of gross domestic product (gdp) in a state going toward health care in 2009, we use the function ( f(x) = 1.5 ln x + 12.1 ), where ( f(x) ) is the percentage of gross domestic product going toward health care ( x ) years after 2006.

part a

determine the percentage of gross domestic product that went toward health care in 2009.

part b

does this underestimate or overestimate the percent displayed by the graph? by how much?

(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 2007 is the starting point (let's assume x = 0 for 2007), then 2009 is 2 years after 2007, so x = 2.

Step2: Substitute x = 2 into the function f(x) = 1.5 ln x + 12.1

First, calculate ln(2). We know that $\ln(2) \approx 0.6931$. Then, $1.5 \times \ln(2) \approx 1.5 \times 0.6931 = 1.03965$. Then add 12.1: $f(2) = 1.03965 + 12.1 = 13.13965$.

Step3: Round to the nearest tenth

Rounding 13.13965 to the nearest tenth gives 13.1. Now, from the graph, the percentage for 2009 is 14.1. Since 13.1 < 14.1, the function underestimates the percentage.

Answer:

The percentage of GDP for health care in 2009 using the function is approximately 13.1, and the function underestimates the percentage shown by the graph (which is 14.1).