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 expense, 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 percentage 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 39 %. which is the same as the percentage on the bar graph.
b. use the function to project the percentage of adults who will put off medical treatment because of expense in 2023.
the percentage of adults who will put off medical treatment because of expense in 2023 will be % .
(round to the nearest percent as needed.)

Explanation:

Step1: Identify the year for 2023

First, we need to determine the value of \( x \) for the year 2023. Since \( x \) represents the number of years after 2000, for 2023, \( x = 2023 - 2000 = 23 \).

Step2: Substitute \( x = 23 \) into the function

The function is \( f(x)=5.3\ln x + 19 \). Substitute \( x = 23 \) into the function:
First, calculate \( \ln(23) \). We know that \( \ln(23)\approx3.1355 \) (using a calculator for the natural logarithm of 23).
Then, calculate \( 5.3\times\ln(23) \): \( 5.3\times3.1355\approx5.3\times3.1355 = 16.61815 \).
Next, add 19 to this result: \( 16.61815 + 19 = 35.61815 \).

Step3: Round to the nearest percent

Rounding \( 35.61815 \) to the nearest percent gives us 36.

Answer:

36