Halliday, Resnick & Walker — Measurement: Problem 55

Dog years. Dog owners like to convert the age of a dog (dubbed dog years) to the usual meaning of years to account for the more rapid aging of dogs. One measure of the aging process in both dogs and humans is the rate at which the DNA changes in a process called methylation. Research on that process shows that after the first year, the equivalent age of a dog is given by \[\text{equivalent age} = 16 \ln(\text{dog years}) + 31,\] where \(\ln\) is the natural logarithm. What then is the equivalent age of a dog on its 13th birthday?