Question

the bar graph shows the percentage of adults putting off medical treatment in seven selected years because of expense. the function f(x) = 5.3 ln x + 19 models the percentage of adults putting off medical treatment because of the expense, f(x), x years after 2000. answer parts (a) and (b).
a. use the function to find the percentage of adults who put off medical treatment because of expense in 2019. how well does this rounded function value estimate the percent displayed by the graph?
select the correct choice below and fill in the answer box(es) to complete your choice.
(round to the nearest percent as needed.)
a. the percentage of adults who will put off medical treatment because of expense in 2019 is %. so, the function underestimates the actual percentage by %.
b. the percentage of adults who will put off medical treatment because of expense in 2019 is %. so, the function overestimates the actual percentage by %.
c. the percentage of adults who will put off medical treatment because of expense in 2019 is %, which is the same as the percentage on the bar graph.

(bar graph titled percentage of adults putting off medical treatment because of expense with years 2001, 2004, 2007, 2010, 2013, 2016, 2018 and corresponding percentages 19, 26, 29, 31, 33, 34, 35)

Explanation:

Step1: Identify x for 2019

x is years after 2000, so 2019 - 2000 = 19. So x = 19.

Step2: Substitute x into f(x)

The function is \( f(x) = 5.3\ln x + 19 \). Substitute x = 19:
First, calculate \( \ln(19) \approx 2.9444 \).
Then, \( 5.3 \times 2.9444 \approx 15.6053 \).
Add 19: \( 15.6053 + 19 = 34.6053 \approx 35 \) (rounded to nearest percent).
Now, check the bar graph for 2019 (which is 2018? Wait, the graph has 2018 with 35? Wait, the years are 2001,2004,2007,2010,2013,2016,2018. Wait, maybe 2019 is approximated, but the graph's 2018 is 35. So the function's estimate for x=19 (2019) is 35, and the graph's 2018 (close to 2019) is 35? Wait, no, let's recheck. Wait, the function is for x years after 2000. So 2019 is x=19. The graph: 2018 is x=18 (2018-2000=18). Wait, maybe the graph's 2018 is 35. Let's see the options. Option C says "the same as the bar graph". So when we calculate f(19) ≈ 35, and if the bar graph for 2018 (x=18) or 2019 (x=19) is 35, then it's the same. So the percentage in 2019 is 35, which is same as bar graph. So option C.

Answer:

C. The percentage of adults who will put off medical treatment because of expense in 2019 is 35%, which is the same as the percentage on the bar graph.