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Hitman42 [59]
3 years ago
13

The rate of change in sales for Garmin from 2008 through 2013 can be modeled by

Mathematics
1 answer:
Zina [86]3 years ago
7 0

Answer:

a) The model for the sales of Garmin is represented by S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + 47.112.

b) The average sales of Garmin from 2008 through 2013 were $ 2.5 billion.

Step-by-step explanation:

a) The model for the sales of Garmin is obtained by integration:

S(t) = -0.0972\int {t^{2}} \, dt + 2.136\int {t}\,dt -11.9 \int\,dt

S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + C (1)

Where C is the integration constant.

If we know that t = 9 and S(t) = 2.9, then the model for the sales of Garmin is:

-\frac{81}{2500} \cdot 9^{3} + \frac{267}{250}\cdot 9^{2}-11.9\cdot (9) + C = 2.9

C = 47.112

The model for the sales of Garmin is represented by S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + 47.112.

b) The average sales of the Garmin from 2008 through 2013 (\bar{S}) is determined by the integral form of the definition of average, this is:

\bar{S} = \frac{1}{13 - 8} \cdot \int\limits^{13}_{8} {S(t)} \, dt (2)

\bar S = \frac{1}{5}\cdot \int\limits^{13}_{8} {\left[-\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2}-11.9\cdot t + 47.112  \right]} \, dt

\bar S = \frac{1}{5}\cdot \left[-\frac{81}{10000}\cdot (13^{4}-8^{4}) +\frac{89}{250}\cdot (13^{3}-8^{3}) -\frac{119}{20}\cdot (13^{2}-8^{2}) +47.112\cdot (13-8)   \right]\bar{S} = \frac{1}{5}\cdot (-198.167+599.86-624.75+235.56)

\bar{S} = 2.5

The average sales of Garmin from 2008 through 2013 were $ 2.5 billion.

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