Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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The following table shows national health care costs, measured in billions of dollars.
1980 1990 2000 2010
1970
75
253 714 1353 2570
Date
Costs in
billions
(a) Plot the data. (Lett be years since 1970 and H the costs in billions of dollars.)
H
H
2500
2000
1500
1000
O
500
H
2500
2000
1500
O
1000
500
10
10
20
20
30
30
40
40
t
t
2500
2000
1500
1000
O
500
H
2500
2000
1500
O
1000
500
10
10
20
20
30
30
40
Estimate that value. (Use the model found in part (b). Round your answer to the nearest integer.)
billion dollars
40
t
(b) Find an exponential function that approximates the data for health care costs. (Let t be years since 1970 and H the costs in billions of dollars.)
OH 94.414 x 1.091¹
OH = 3120.372 x 0.916*
H = 72.438 x 1.143
H = 993.002 * 1.002
OH = 2560.371 x 0.872²
(c) By what percent per year were national health care costs increasing during the period from 1970 through 2010? (Use the model found in part (b). Round your answer to one decimal place.)
1%
(d) Use functional notation to express how much money was spent on health care in the year 2014. (Lett be years since 1970.)
H(D
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Transcribed Image Text:The following table shows national health care costs, measured in billions of dollars. 1980 1990 2000 2010 1970 75 253 714 1353 2570 Date Costs in billions (a) Plot the data. (Lett be years since 1970 and H the costs in billions of dollars.) H H 2500 2000 1500 1000 O 500 H 2500 2000 1500 O 1000 500 10 10 20 20 30 30 40 40 t t 2500 2000 1500 1000 O 500 H 2500 2000 1500 O 1000 500 10 10 20 20 30 30 40 Estimate that value. (Use the model found in part (b). Round your answer to the nearest integer.) billion dollars 40 t (b) Find an exponential function that approximates the data for health care costs. (Let t be years since 1970 and H the costs in billions of dollars.) OH 94.414 x 1.091¹ OH = 3120.372 x 0.916* H = 72.438 x 1.143 H = 993.002 * 1.002 OH = 2560.371 x 0.872² (c) By what percent per year were national health care costs increasing during the period from 1970 through 2010? (Use the model found in part (b). Round your answer to one decimal place.) 1% (d) Use functional notation to express how much money was spent on health care in the year 2014. (Lett be years since 1970.) H(D
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