the sales of a certain product after an initial release can be found by the equation s = 12 square root of 4t+10, where s represents the total sales (in thousands) and t repersents the time in weeks after realease. make a tabe of values, graph the function and use the graph to estimate the sales 8 weeks after release
To make a table of values, we substitute different values for t into the equation and calculate the corresponding values of s:
When t = 0,
s = 12√(4(0) + 10)
s = 12√(10)
s ≈ 12 * 3.16
s ≈ 37.92
When t = 1,
s = 12√(4(1) + 10)
s = 12√(14)
s ≈ 12 * 3.74
s ≈ 44.88
When t = 2,
s = 12√(4(2) + 10)
s = 12√(18)
s ≈ 12 * 4.24
s ≈ 50.88
When t = 3,
s = 12√(4(3) + 10)
s = 12√(22)
s ≈ 12 * 4.69
s ≈ 56.28
When t = 4,
s = 12√(4(4) + 10)
s = 12√(26)
s ≈ 12 * 5.10
s ≈ 61.20
When t = 5,
s = 12√(4(5) + 10)
s = 12√(30)
s ≈ 12 * 5.48
s ≈ 65.76
Now let's graph the function:
The graph of the equation s = 12√(4t + 10) will be a curve. As t increases, s will also increase, but at a decreasing rate.
Using the graph, we can estimate the sales 8 weeks after the release by finding the point where t = 8 on the x-axis and then looking at the corresponding value of s on the y-axis.