Questions: Among all deaths from a disease, the percentage that are smoking-related is a function of the disease's incidence ratio, the number of times more likely smokers are than nonsmokers to die from the disease. The table to the right shows incidence ratios for a particular group. The rational function P(x) models the percentage of smoking-related deaths among all deaths from a disease, P(x), in terms of the disease's incidence ratio, x. The graph of P(x) is shown to the right. Age Incidence Ratios Heart Disease Lung Cancer ------------------------------------------------ 55-64 1.9 65-74 1.7 8 Find P(7). P(7)= (Round to the nearest integer as needed.)

Among all deaths from a disease, the percentage that are smoking-related is a function of the disease's incidence ratio, the number of times more likely smokers are than nonsmokers to die from the disease. The table to the right shows incidence ratios for a particular group. The rational function P(x) models the percentage of smoking-related deaths among all deaths from a disease, P(x), in terms of the disease's incidence ratio, x. The graph of P(x) is shown to the right.

Age  Incidence Ratios Heart Disease  Lung Cancer
------------------------------------------------
55-64  1.9  
65-74  1.7  8

Find P(7).

P(7)=

(Round to the nearest integer as needed.)
Transcript text: Among all deaths from a disease, the percentage that are smoking-related is a function of the disease's incidence ratio, the number of times more likely smokers are than nonsmokers to die from the disease. The table to the right shows incidence ratios for a particular group. The rational function $\mathrm{P}(\mathrm{x})$ models the percentage of smoking-related deaths among all deaths from a disease, $\mathrm{P}(\mathrm{x})$, in terms of the disease's incidence ratio, x . The graph of $\mathrm{P}(\mathrm{x})$ is shown to the right. \begin{tabular}{|l|c|c|} \hline Age & \multicolumn{2}{|c|}{\begin{tabular}{c} Incidence Ratios \\ Heart \\ Disease \end{tabular}} \\ \hline $55-64$ & 1.9 & \begin{tabular}{c} Lung \\ Cancer \end{tabular} \\ \hline $65-74$ & 1.7 & 8 \\ \hline \end{tabular} Find $\mathrm{P}(7)$. \[ P(7)= \] $\square$ (Round to the nearest integer as needed.)
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Solution

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Solution Steps

Step 1: Identify the function

The given function is P(x) = 100(x-1)/x.

Step 2: Substitute the value of x

Substitute x = 7 into the function: P(7) = 100(7-1)/7

Step 3: Calculate P(7)

P(7) = 100(6)/7 P(7) = 600/7 P(7) ≈ 85.71

Step 4: Round to the nearest integer

Rounding to the nearest integer, we get 86.

Final Answer

86

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