Question

In a population, the frequency of an allele changes with time as shown in the table below.

Year (x)	0	10	20	30	40
Allele frequency (y)	0.1	0.2	0.3	0.4	0.5

Which one of the following describes how allele frequency changes with year?

• A. \(y = 0.01x + 0.1\)
• B. \(x = y + 0.1\)
• C. \(x = 0.1 + 0.01y\)
• D. \(y = x + 0.1\)

Hint:

Find the slope from any two points in the table, then check which equation matches both the slope and the intercept.

Answer 1

The Correct Option is A

Step 1: Read off the points from the table.
The table gives pairs of (year, allele frequency):
\[ (0,\,0.1),\ (10,\,0.2),\ (20,\,0.3),\ (30,\,0.4),\ (40,\,0.5) \]

Step 2: Check if the points fall on a straight line.
Look at how much \(y\) changes each time \(x\) increases by \(10\):
\[ 0.2-0.1=0.1,\quad 0.3-0.2=0.1,\quad 0.4-0.3=0.1,\quad 0.5-0.4=0.1 \]
Since \(y\) goes up by the same amount, \(0.1\), every time \(x\) goes up by \(10\), the points lie on a straight line.

Step 3: Find the slope.
\[ \text{slope}=\frac{\Delta y}{\Delta x}=\frac{0.1}{10}=0.01 \]

Step 4: Find the intercept.
At \(x=0\), the table gives \(y=0.1\). Since the line has the form \(y=mx+c\), plugging in \(x=0\) gives \(c=0.1\) directly.

Step 5: Write the full equation and check it.
\[ y=0.01x+0.1 \]
Check with \(x=40\):
\[ y=0.01(40)+0.1=0.4+0.1=0.5 \]
This matches the table exactly.

Step 6: Rule out the other options.
\(x=y+0.1\) and \(x=0.1+0.01y\) both write \(x\) as a function of \(y\) with the wrong scaling, and fail when checked against the table, for example at \(y=0.1\), \(x=y+0.1\) gives \(x=0.2\), not \(0\). \(y=x+0.1\) fails too, since at \(x=0\) it gives \(y=0.1\) correctly but at \(x=10\) it wrongly gives \(y=10.1\) instead of \(0.2\).

Step 7: Final answer.
\[ \boxed{y=0.01x+0.1} \]