1. An alien space baby is born on Year Zero. At birth, the baby is 10 cm tall. The baby grows 1 cm taller per month, or 12 cm per year. If x is the time in years after Year Zero, write an equation that describes the height of the baby as a function of the year.

2. How tall is the alien space baby of problem 1 at the age of 5 years?

3. How tall is the alien space baby of problem 1 at the age of 30 years?

Bonus question: if the alien space baby looks human, when would people start to suspect that the alien space baby is an alien?

4. Betty’s sequoia tree grows one ring per year. Let x be the current year (2014). Betty takes a core sample and finds out that her tree has 157 rings in the year 2014. Write an equation that describes the number of rings in the sequoia tree as a function of the calendar year x.

Bonus: what year was the sequoia tree born?

5. The equation for the number of rings in Betty’s sequoia tree as a function of calendar year, when you graph it, is the equation of a straight line. Does Betty’s sequoia tree grow in a manner similar to the alien space baby? Why or why not?

Some things to think about: how does a typical human grow? What would your own human height as a function of age look like, compared to the alien space baby’s? What are some different ways to measure the growth of a tree? What if, instead of rings, you measured the tree’s gain in diameter each year – what kind of function would that be?

Answers