Medicare. The annual expenditures for Medicare (in billions of dollars) by the U.S. government for selected years since 1980 are shown in Table 5 . Let x represent years since 1980 . (A) Find an exponential regression model y = a b x for the data. Estimate (to the nearest billion) the annual expenditures in 2025 . (B) When will the annual expenditures exceed two trillion dollars?
Medicare. The annual expenditures for Medicare (in billions of dollars) by the U.S. government for selected years since 1980 are shown in Table 5 . Let x represent years since 1980 . (A) Find an exponential regression model y = a b x for the data. Estimate (to the nearest billion) the annual expenditures in 2025 . (B) When will the annual expenditures exceed two trillion dollars?
Medicare. The annual expenditures for Medicare (in billions of dollars) by the U.S. government for selected years since
1980
are shown in Table
5
. Let
x
represent years since
1980
.
(A) Find an exponential regression model
y
=
a
b
x
for the data. Estimate (to the nearest billion) the annual expenditures in
2025
.
(B) When will the annual expenditures exceed two trillion dollars?
3. [-/2 Points]
DETAILS
MY NOTES
SESSCALCET2 7.4.013.
Find the exact length of the curve.
y = In(sec x), 0 ≤ x ≤ π/4
Calculate a = x+y, b = z + 1, then keep numbers a and b.
Questions marked with *** are to be graded.
1. Use the initial and final value theorems to determine x(0*) and x(oo) for the following
transforms:
a(s+2)
***
a) X(s)=
s(s+b)
2(s+2)
b) X(s)=
s(s+a)(s+b)
2. Obtain the inverse Laplace transform for the following transforms.
a) F(s)=
as+b
b) F(s)=
5s+2
(s+a)(s+b)²
3. Obtain the solution x(t) of the the following differential equations:
a) x+ax=0, x(0)=b, x(0) = 0
b) 2x+2x+x=a, x(0)=0, x(0)=b
4. Obtain the inverse transform of the following. If the denominator of the transform has
complex roots, express x(t) in terms of sin() and cos().
***
a) X(s)=
b) X(s)=
4s+a
+8s+b
s³+as+6
s(s+b)
5. Determine the unit-step response, f (t) = u(t) of the following models. Take zero initial
conditions.
a) ax+20x+bx = f(t)
b) x+ax+bx=3f(t)+2f(t)
In a survey, the planning value for the population proportion is p 0.25. How large a sample should be taken to provide a 95% confidence interval with a margin of error
of 0.03? Round your answer up to the next whole number.
800
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