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Linear Modelling2018-12-03T17:31:06+10:00

Maths Made Easy Forums Standard Linear Relationships Linear Modelling

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At a day care centre, the number of words that each child can use is estimated and recorded. The age of each child is also recorded. The graph shows these results.
a. Draw the line of best fit through the plotted
b. Sally, who is three-and-a-half years old, was away from the centre on the day that this data was collected. Use your line of best fit to predict the number of words in Sally’s vocabulary.
c. From the graph, estimate at what age a child begins to use words.
d. Use your graph to estimate the average rate at which the number of words increases per year.
e. Would you expect this trend to continue as the child progresses into adulthood? Justify your answer.

a.

b. approximately 1250 (this will vary depending on your line)

c. approximately 1.8 years (find the x-intercept. this will vary depending on the line you have drawn, so they are only estimates)

d. average rate is the gradient = $\frac{rise}{run}$

$=\frac{2500}{5.8-1.8}$

= 625

(remember this will vary from graph to graph, so numbers close to this are fine)

e. no, as we learn at much faster rates when we are young, and once in high school, our vocabulary will stabilise and nowhere near as many new words will be learnt

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