Annual sales of bottled water in the country in the period 1993 - 2003 could be approximated by the function R(t)=10t∗2+100t+2400R(t)=10t∗2+100t+2400 (million gallons) where t is time in years since 1990

Marketing Dec 20, 2020

Annual sales of bottled water in the country in the period 1993 - 2003 could be approximated by the function R(t)=10t∗2+100t+2400R(t)=10t∗2+100t+2400 (million gallons) where t is time in years since 1990. Were sales of bottled water accelerating or decelerating in 2000? How fast?

Expert Solution

Given that:

Annual sales of bottled water in the country in the period 1993−20031993−2003 could be approximated by the function;

R(t)=10t2+100t+2400R(t)=10t2+100t+2400.

The time period between 1993−20031993−2003 is 0≤t≤100≤t≤10.

Differentiate the function R(t)R(t) with respect to tt:

R′(t)=d(10t2+100t+2400)dx=20t+100+0∴R′(t)=20t+100R′(t)=d(10t2+100t+2400)dx=20t+100+0∴R′(t)=20t+100

Again differentiate R′(t)R′(t) with respect to tt:

R′′(t)=20R″(t)=20

Therefore, annual sales of bottled water is accelerating 20 million gallons per year20 million gallons per year in 20002000

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