Problem

Problem of the Week
Problem B
It’s Been A Dog’s Age

A new way to relate a dog’s age to a human’s age, based on researchers studying labrador retrievers, is discussed at www.caninejournal.com/dog-years-to-human-years. The relationship they found is shown in the graph below.

A description of the graph follows.

A graph entitled Relationship Between Dog Age and Human Age. The horizontal axis is Dog Age (in years) and ranges from $0$ to $14$ . The vertical axis is Human Age (in years) and ranges from $0$ to $100$ . The graph is a curved line that starts at $(0, 0)$ and ends at approximately $(14, 73)$ . The curved line shows a steep increase in Human Age from Dog Age $0$ to $2$ , then a more gradual increase from $2$ to $6$ , and then an even more gradual increase from $6$ to $14$ . The following table provides an approximate data point for each Dog Age on the graph.

Dog Age (years)	Human Age (years)
$0$	$0$
$1$	$31$
$2$	$42$
$3$	$49$
$4$	$53$
$5$	$57$
$6$	$60$
$7$	$62$
$8$	$64$
$9$	$66$
$10$	$68$
$11$	$69$
$12$	$71$
$13$	$72$
$14$	$73$

A traditional way to relate a dog’s age to a human’s age is by multiplying the dog’s age by $7.$ This comparison is called linear because its graph is a straight line. Since multiplication by $7$ implies that $14$ years of dog age equals $7 \times 14 = 98$ years of human age, this line will go from $(0, 0)$ to $(14, 98) .$ Sketch this line carefully on the given graph.

For dog ages of $2$ , $6$ , and $10$ years, use your graph to estimate the human age predicted the traditional way and the new way.

For what dog age are the two predicted human ages farthest apart? About how many years apart are the two predicted human ages?

For what dog ages are the two predicted human ages the same?

If the first year of a cat’s life is equivalent to $15$ human years, the second year to $9$ human years, and each year thereafter to $4$ human years, then show that by the age of $6$ a cat will be younger in human years than either of the predicted dog ages in human years.

Theme: Data Management

Problem of the Week Problem B It’s Been A Dog’s Age

Problem of the Week
Problem B
It’s Been A Dog’s Age