For this exercise, round all regression parameters to three decimal places. The following table shows national health care costs, measured in billions of dollars. 1970 1980 1990 2000 2010 253 714 1353 2570 75 Date Costs in billions (a) Plot the data. (Lett be years since 1970 and the costs in billions of dollars.) H H 2500 2000 1500 1000 500 H 2500 2000 1500 1000 500 10 10 20 20 30 30 40 40 2500 2000 1500 1000 500 H 2500 2000 1500 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 't (b) Find an exponential function that approximates the data for health care costs. (Lett be years since 1970 and H the costs in billions of dollars.) OH-94.414 1.091 OH-3120.372 x 0.916 OH-72.438 x 1.143 OH-993.002 1.002² OH-2560.371 * 0.872 (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.) (d) Use functional notation to express how much money was spent on health care in the year 2014. (Lett be years since 1970.)
For this exercise, round all regression parameters to three decimal places. The following table shows national health care costs, measured in billions of dollars. 1970 1980 1990 2000 2010 253 714 1353 2570 75 Date Costs in billions (a) Plot the data. (Lett be years since 1970 and the costs in billions of dollars.) H H 2500 2000 1500 1000 500 H 2500 2000 1500 1000 500 10 10 20 20 30 30 40 40 2500 2000 1500 1000 500 H 2500 2000 1500 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 't (b) Find an exponential function that approximates the data for health care costs. (Lett be years since 1970 and H the costs in billions of dollars.) OH-94.414 1.091 OH-3120.372 x 0.916 OH-72.438 x 1.143 OH-993.002 1.002² OH-2560.371 * 0.872 (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.) (d) Use functional notation to express how much money was spent on health care in the year 2014. (Lett be years since 1970.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:For this exercise, round all regression parameters to three decimal places.
The
following table shows national health care costs, measured in billions of dollars.
1970 1980 1990 2000 2010
75 253 714 1353 2570
Date
Costs in
billions
(a) Plot the data. (Lett be years since 1970 and the costs in billions of dollars.)
H
H
2500
2000
1500
1000
500
H
2500
2000
1500
1000
500
10
10
20
20
30
30
40
40
2500
2000
1500
1000
500
H
2500
2000
1500
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. (Lett be years since 1970 and H the costs in billions of dollars.)
OH-94.414 x 1.091¹
OH-3120.372 x 0.916
OH-72.438 x 1.143
OH-993.002 * 1.002²
OH-2560.371 × 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.)
(d) Use functional notation to express how much money was spent on health care in the year 2014. (Lett be years since 1970.)
Transcribed Image Text:You initially invest $400 in a savings account that pays a yearly interest rate of 3%.
(a) Write a formula for an exponential function giving the balance in your account as a function of the time since your initial investment. (Let B be the account balance in dollars and to be the number of years since the initial investment.)
dollars
B(t) =
(b) What monthly interest rate best represents this account? Round your answer to three decimal places.
%
(c) Calculate the decade growth factor. (Round your answer to two decimal places.)
(d) Use the formula you found in part (a) to determine how long it will take for the account to reach $536. (Round your answer to the nearest whole number.)
lyr
Explain how this is consistent with your answer to part (c).
At the end of one decade, there will be $
This F
the answer found above where the account reaches $536 at the end of
years.
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