A biologist observed a curved relationship between the average heart rates and life expectancies of several
mammal species in a large sample. The biologist took the natural logarithm for the values of both variables,
and they noticed a linear relationship in the transformed data.
Here's the least-squares regression equation for the transformed data, where life expectancy (LE) is in
years and heart rate (HR) is in beats per minute.
In(LE
6.33 – 0.78 In(HR)
According to this model, what is the predicted life expectancy of a mammal species whose average heart
rate is 200 beats per minute?
You may round your answer to the nearest whole year.
years
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jane96583 jane96583 · Answer 1 · 2021-04-26T02:46:35+02:00

Answer:

9 years

Step-by-step explanation:

According to khan academy

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joaobezerra joaobezerra · Answer 2 · 2021-10-12T13:05:03+02:00

Applying the logarithmic function, it is found that the life expectancy of the mammal specie is of 9 years.

The life expectancy(LE) of a specie with heart rate HR is given by the following logarithmic function below:

[tex]\ln{LE} = 6.33 - 0.78\ln{HR}[/tex]

In this problem, heart rate of 200 beats per minute, thus [tex]HR = 200[/tex].

The life expectancy is:

[tex]\ln{LE} = 6.33 - 0.78\ln{HR}[/tex]

[tex]\ln{LE} = 6.33 - 0.78\ln{200}[/tex]

[tex]\ln{LE} = 2.19731245409[/tex]

[tex]e^{\ln{LE}} = e^{2.19731245409}[/tex]

[tex]LE = 9[/tex]

Life expectancy of 9 years.

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