Question

the bar graph shows the percentage of adults putting off medical treatment in seven selected years because of expense. the function f(x)=5.7 ln x + 18 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 35 %, which is the same as the percentage on the bar graph.
c. the percentage of adults who will put off medical treatment because of expense in 2019 is %. so, the function overestimates the actual percentage by %.
b. use the function to project the percentage of adults who will put off medical treatment because of expense in 2024.
the percentage of adults who will put off medical treatment because of expense in 2024 will be %.
(round to the nearest percent as needed.)

Explanation:

Step1: Calculate x for 2019

For the year 2019, $x = 2019 - 2000=19$.

Step2: Find f(x) for 2019

Substitute $x = 19$ into $f(x)=5.7\ln x + 18$.
$f(19)=5.7\ln(19)+18$.
Since $\ln(19)\approx2.9444$, then $f(19)=5.7\times2.9444 + 18$.
$5.7\times2.9444=16.78308$, and $f(19)=16.78308 + 18=34.78308\approx35$.

Step3: Calculate x for 2024

For the year 2024, $x = 2024 - 2000 = 24$.

Step4: Find f(x) for 2024

Substitute $x = 24$ into $f(x)=5.7\ln x+18$.
Since $\ln(24)\approx3.1781$, then $f(24)=5.7\times3.1781+18$.
$5.7\times3.1781 = 18.11517$, and $f(24)=18.11517+18=36.11517\approx36$.

Answer:

a. B. 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.
b. 36