Question 971639: A book publisher estimates that the total number of sales of a
particular book, after the first 15 weeks, can be modelled by the linear
equation
s = 1400(t − 15) + 150 000 (t ≥ 15),
where s is the total number of sales, and t is the time on sale in weeks
(i) Find the number of sales after 24 weeks
(ii) Calculate the week at which the total number of sales reaches
171 000
(iii) Write down the gradient of the straight line represented by the
equation
s = 1400(t − 15) + 150 000
What does this measure in the practical situation being modelled?
(iv) Explain why the vertical s-intercept of a graph of s is not 150 000
Answer by amarjeeth123(569)   (Show Source):
You can put this solution on YOUR website! s = 1400(t − 15) + 150 000 (t ≥ 15)
Plugging in the values we get,
(i)Number of sales after 24 weeks s=1400(24-15)+150000=1400(9)+150000=12600+150000=162600
(ii)171000=1400(t − 15)+150000
1400(t-15)=21000
t-15=15
t=30
(iii)s=1400(t−15)+150000
s=1400t+129000
Comparing this with y=mx+c we get,
The gradient of the straight line is 1400.
This measures the incremental rate of publishing the book per week.
(iv)The vertical intercept of the graph is 129000.
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