Bottled Water Sales Annual U.S. per capita sales of bottled water in the period 2007–2014 could be approximated by R ( t ) = 0.25 t 2 − t + 29 gallons ( 0 ≤ t ≤ 7 ) , where t is time in years since 2007. According to the model, were annual U.S. per capita sales of bottled water accelerating or decelerating in 2009? How fast? [ HINT: See Example 2.]
Bottled Water Sales Annual U.S. per capita sales of bottled water in the period 2007–2014 could be approximated by R ( t ) = 0.25 t 2 − t + 29 gallons ( 0 ≤ t ≤ 7 ) , where t is time in years since 2007. According to the model, were annual U.S. per capita sales of bottled water accelerating or decelerating in 2009? How fast? [ HINT: See Example 2.]
Solution Summary: The author calculates whether the annual sales of bottled water in the united states were accelerating or decelerating in 2009.
Bottled Water Sales Annual U.S. per capita sales of bottled water in the period 2007–2014 could be approximated by
R
(
t
)
=
0.25
t
2
−
t
+
29
gallons
(
0
≤
t
≤
7
)
,
where t is time in years since 2007. According to the model, were annual U.S. per capita sales of bottled water accelerating or decelerating in 2009? How fast? [HINT: See Example 2.]
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
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