Chapter 8.2, Problem 40E

a.

To determine

To approximate:

The age of Suiko to the nearest tenth of a million years, if Suiko is 4794 kilometers from Kilauea.

Answer to Problem 40E

The age of Suiko would be approximately 59.6 million years.

Explanation of Solution

Given:

The Hawaiian-Emperor chain of volcanoes is shown below.

The age a (in millions of years) of a volcano in the chain can be approximated by $a=0.0129d-2.25$ , where d is the volcano’s distance (in kilometers) from Kilauea, measured along the chain.

  

Calculation:

To find Suiko’s age, we will substitute $d=4794$ in our given formula as:

  $\begin{array}{l}a=0.0129d-2.25\left(\text{Given formula}\right)\\ a=0.0129(4794)-2.25\left(\text{Substituting }d=4794\right)\\ a=61.8426-2.25\\ a=59.592645\\ a\approx 59.6\left(\text{Rounding to nearest tenth}\right)\end{array}$

Therefore, the age of Suiko would be approximately 59.6 million years.

b.

To determine

To approximate:

Midway’s distance along the chain from Kilaueato the nearest ten kilometers, if Midawayis about 27.7 million years old.

Answer to Problem 40E

Midway’s distance along the chain from Kilauea would be approximately 2320kilometers.

Explanation of Solution

Given:

The Hawaiian-Emperor chain of volcanoes is shown below.

The age a (inmillions of years) of a volcano in the chain can be approximated by $a=0.0129d-2.25$ , where d is the volcano’s distance (in kilometers) from Kilauea, measured along the chain.

  

Calculation:

To find Midway’s distance along the chain from Kilauea, we will substitute $a=27.7$ in our given formula as:

  $\begin{array}{l}a=0.0129d-2.25\left(\text{Given formula}\right)\\ 27.7=0.0129d-2.25\left(\text{Substituting }a=27.7\right)\\ 0.0129d-2.25=27.7\left(\text{Switching sides}\right)\\ 0.0129d-2.25+2.25=27.7+2.25\left(\text{Adding 2}\text{.25 on both sides}\right)\\ 0.0129d=29.9556\\ \frac{0.0129d}{0.0129}=\frac{29.9556}{0.0129}\left(\text{Dividing both sides by }0.0129\right)\\ d=2321.70542636\\ d\approx 2320\left(\text{Rounding to nearest tens}\right)\end{array}$

Therefore, Midway’s distance along the chain from Kilauea would be approximately 2320 kilometers.