Question

Rip van Winkle has fallen asleep for a very long time.
The length of his beard (in millimeters) as a function of time (in weeks) is graphed.
graph
How long did it take each time Rip van Winkle's beard grew by 5 millimeters?

Choose 1 answer:
2 weeks
2.5 weeks
7.5 weeks
5 weeks

Answer 1

Answer:

2 weeks.

Step-by-step explanation:

We can solve this problem by just using the given graph.

Notice that the straight line starts at $y=10$, that means in week zero the beard was 10 millimeters long.

First, let's find the constant ratio of change, using two points (0,10) and (20,60)

$r=\frac{60-10}{20-0}=\frac{50}{20}=\frac{5}{2} =2.5$

According to the ratio, every 5 millimeter grows each 2 weeks, in other words, the ratio of growth is 2.5 millimeters per week.

Therefore, the right answer is 2 weeks.

Answer 2

For the beard to grow by 5 mm, it would take 2 weeks.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

Let y represent the beard length in mm and x represent the time in weeks.

From the graph, the line passes through (0, 10) and (10, 35). Hence:

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{35-10}{10-0}(x-0)\\\\y=2.5x+10$

For the beard to grow by 5 mm, it would take 2 weeks.

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