Using Exponential Regression to Fit a Model to Data
In 2007, a university study was published investigating the crash risk of alcohol impaired driving. Data from 2,871 crashes were used to measure the association of a person’s blood alcohol level (BAC) with the risk of being in an accident. The table shows results from the study. The relative risk is a measure of how many times more likely a person is to crash. So, for example, a person with a BAC of 0.09 is 3.54 times as likely to crash as a person who has not been drinking alcohol.
(a) Let represent the BAC level, and let represent the corresponding relative risk. Use exponential regression to fit a model to these data.
(b) After 6 drinks, a person weighing 160 pounds will have a BAC of about How many times more likely is a person with this weight to crash if they drive after having a 6-pack of beer? Round to the nearest hundredth.
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OpenStax, Algebra and Trigonometry 2e · §6.8 Fitting Exponential Models to Data · Example 3
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