Can you solve #18 from practice test 5 calculator section? Thank you.

Sure. We can approximate the age of each tree using the table provided (the paragraph under the table says so). So a white birch tree with a diameter of 12 inches is approximately 12\times 5.0=60 years old and a pin oak tree with a diameter of 12 inches is approximately 12\times 3.0=36 years old. (You actually don’t need to do this for this question because on the test you would have figured these mechanics out on question 16 but I’m including it here for completeness’s sake.)

Now, note that the concept of a “growth factor” as provided in the table only works if the trees grow at roughly a constant rate. That means that we can incorporate units into the multiplication we just did, which helps clarify how everything is working. If we’re multiplying a diameter in inches by a growth factor and getting an output in years, what must be the units of the growth factor?

12\text{ inches}\times 5.0\text{ [???]}=60\text{ years}

The only thing you can multiply inches by to get years is \frac{\text{years}}{\text{inches}}!

12\text{ inches}\times 5.0\:\dfrac{\text{years}}{\text{inches}}=60\text{ years}

What the “growth factor” really tells us, then, is how many years it takes a species of tree to grow an inch: it takes a white birch tree 5.0 years to grow an inch and it takes a pin oak tree 3.0 years to grow an inch.We can DIVIDE a number of years by the growth factor to see how many inches a tree would grow in that many years!

10\text{ years}\div 5.0\:\dfrac{\text{years}}{\text{inches}}=2\text{ inches}

10\text{ years}\div 3.0\:\dfrac{\text{years}}{\text{inches}}=3.33...\text{ inches}

So in 10 years a white birch tree will have grown 2 inches and a pin oak tree will have grown about 3.3 inches. Since the two trees we were starting with both had a diameter of 12 inches, their new diameters will be about 12+2=14 inches and 12+3.3 =15.3 inches, respectively. That’s a difference of about 1.3 inches.