Math  /  Data & Statistics

QuestionIn 2015, 88%88 \% of U.S. residents used the internet, up from 14%14 \% in 1995. The table shows the percent who use the internet for selected years from 2000 and projected to 2025. \begin{tabular}{cc|cc} \hline Year & Percent & Year & Percent \\ \hline 2000 & 67 & 2015 & 88 \\ 2005 & 79 & 2020 & 95 \\ 2010 & 82 & 2025 & 98 \\ \hline \end{tabular} (a) Find the logarithmic function that models the percent pp as a function of xx, the number of years after 1990. Report the model with 4 significant digit coefficients. y=y=\square (b) Visually determine whether this model is a good fit for the data. Yes, this model is a reasonably good fit for the data. No, this model is not a good fit for the data at all. (c) Use the model to predict the percentage of internet users in the United States in 2025. (Round your answer to one decimal place.) \square %\% Need Help? Read It

Studdy Solution
Use the model to predict the percentage in 2025:
x=35 x = 35
p(35)=27.35ln(35)+40.12 p(35) = 27.35 \cdot \ln(35) + 40.12
Calculate p(35) p(35) using a calculator:
p(35)98.1 p(35) \approx 98.1
(a) The logarithmic function is:
y=27.35ln(x)+40.12 y = 27.35 \cdot \ln(x) + 40.12
(b) Visually, the model is a reasonably good fit for the data.
(c) The predicted percentage of internet users in 2025 is:
98.1% \boxed{98.1\%}

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