Heart rates and life spans of most mammals can be modeled...

Heart rates and life spans of most mammals can be modeled using inverse variation. The bar graph shows the average heart rate and the average life span of five mammals. a. A mammal’s average life span, L, in years, varies inversely as its average heart rate, R,in beats per minute. Use the data shown for horses to write the equation that models this relationship. b. Is the inverse variation equation in part (a) an exact model or an approximate model for the data shown for lions? c. Elephants have an average heart rate of 27 beats per minute. Determine their average life span.

Heart rates and life spans of most mammals can be modeled using inverse variation. The bar graph shows the average heart rate and the average life span of five mammals.
a. A mammal’s average life span, L, in years, varies inversely as its average heart rate, R,in beats per minute. Use the data shown for horses to write the equation that models this relationship.
b. Is the inverse variation equation in part (a) an exact model or an approximate model for the data shown for lions?
c. Elephants have an average heart rate of 27 beats per minute. Determine their average life span.

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Key Concepts

Inverse Variation

Inverse variation describes a relationship between two variables where one variable increases as the other decreases so that their product remains constant. This concept is typically expressed with the equation y = k/x, where k is a fixed constant known as the constant of variation.

Constant of Variation

The constant of variation (often represented by k) is the product of the two inversely varying quantities. It's determined using specific data points from a given scenario and remains unchanged across all cases in an ideal inverse relationship.

Mathematical Modeling

Mathematical modeling involves using algebraic equations to represent real-world relationships between variables. In the context of inverse variation, data points are used to establish the equation that predicts one variable based on the other.

Data Interpretation

Data interpretation is the process of analyzing information presented in graphical or tabular formats, such as bar graphs, to extract relevant numerical values and trends. This step is crucial in validating whether a mathematical model accurately represents the behavior of the data.

Transcript

00:01 So we have a list of data and let's just put the summarized in the bar graph into a table.

00:08 And this is the rate in beads per minute.

00:12 And this is the lifespan in years.

00:16 And we have for a squirrel, we have that the beats per minute, 190 and average lifespan 10 years, which surprises me.

00:24 And rabbit, we have the 158.

00:30 And 12 years.

00:33 We have a cat.

00:34 We have 126 and 15 years.

00:40 And for a lion, we have 76 as the rate, and 25 years.

00:48 And naturally, we don't seem to fit into this pattern because for the horse, we have 63 rates per minute and 30 years.

00:58 Now, we know that there's supposed to be an inverse these are inversely proportional.

01:06 And it says, you know, check this out and get a model.

01:08 Okay, so if we know that the length of lifespan is inversely proportional to that heart rate, that means that the product, if i multiply both sides by r, l times r or r times l should equal the constant.

01:27 And so i'm going to multiply r times l and see what those values are.

01:33 And when i do this first one, that one's easy.

01:36 Next one, 1896.

01:38 Very close.

01:40 Next one, 1890.

01:42 Again, very close.

01:43 Next one, 1900...

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