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Chapter 34: Q34.7-6ITD. (page 749)

The slope of a line can be defined asm=y2-y1x2-x1 , where (x1, y1) and (x2, y2) are the co-ordinates of two points on the line. As such, the slope represents the ratio of the rise of a line (how much the line rises vertically) to the run of the line (how much the line changes horizontally). Use the definition of the slope to estimate how long it took for mean brain volume to increase by 100 cm3 over the course of hominin evolution.

Short Answer

Expert verified

About 333 years were required to increase the mean brain volume by 100cm3throughout hominin evolution.

Step by step solution

01

Step 1:The slope of a line

The slope of a line represents the line’s rise to its run. It is calculated by the formula m=y2-y1x2-x1.

Where (x1, y1) and (x2, y2) are the co-ordinates of two points plotted in the graph.

02

Calculation of the slope of the line from the graph

The values of x1=(-1.9), x2=(-1.6), y1=550and y2=850 are determined from the graph.

Substituting these values in the equation of the slope:

m=850-550(-1.6)-(-1.9)m=3000.3m=1000

03

Calculation of time required to increase the mean brain volume by 100 cm3.

According to the definition of the slope, it took 1000 years for the mean brain volume to increase by 300 cm3. Thus, it must have taken approximately 333 (1000/3) years to increase the mean brain volume by 100cm3.

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Most popular questions from this chapter

Redraw Figure 34.2 to show four lineages: cyclostomes, lancelets, gnathostomes, and tunicates. Label the vertebrate common ancestor and circle the lineage that includes humans.

The equation for a regression line can be used to calculate the value of y expected for any particular value of x. For example, suppose that a linear regression indicated that m = 2 and b = 4. In this case, when x = 5. We expect that y= 2x + 4 = (2 × 5) + 4 = 14. Based on the values of m and b that you determined in question 4, use this approach to determine the expected mean brain volume for a hominin that lived 4 million years ago (that is, x = -4)

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(A) reduced jawbones

(B) an enlarged brain

(C) the making of stone tools

(D) bipedal locomotion

Based on the value of r that you calculated in question 2, describe in words the correlation between mean brain volume of hominin species and the mean age of the species.

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