Q41. - Algebra 2

Question

Geologists estimate that the continents of Europe and North America are drifting apart at a rate of an average of 12 miles every 1 million years, or about 0.75 inch per year. If the continents continue to drift apart at that rate, how many inches will they drift in 50 years?

Step-by-Step Solution

Answer

The continents will drift apart 37.5 inches in 50 years.

Step 1. Given Information.

Given Geologists estimate that the continents of Europe and North America are drifting apart at a rate of an average of 12 miles every 1 million years, or about 0.75 inch per year.

Step 2. Calculation .

The n^th term of an arithmetic sequence is given by $a_n=a_1+(n-1)d$ .

 

Here the first term is  $a_1=0.75$

The common difference is  $d=0.75$

And the required term is  $n=50$

 Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_{50}=0.75+(50-1)\left(0.75\right)\\ a_{50}=0.75+\left(49\right)\left(0.75\right)\\ a_{50}=0.75+36.75\\ a_{50}=37.5\end{array}$

Step 3. Conclusion .

Hence, the continents will drift apart 37.5 inches in 50 years.