Out of-pocket spending in a country for health care increased between 2003 and 2008. The function fox)-2574models average annual expenditures per household, in dollars. In this model, x represents the year, where x 0 corresponds to 2003 (a) Estimate out-of-pocket household spending on health care in 2008 (b) Determine the year when spending reached $2875 per household (c) The total expenditures per household in the year 2008 were approximately S (Round to the nearest dollar as needed.)

Answer:

(a) The total expenditures per household in the year 2008 were approximately $3,080.

(b) The spending reached $2875 per household in 2006.

Step-by-step explanation:

Note: This question is not complete, and the part c is not another question but the same question as part a. The complete question is therefore provided before answering the question as follows:

Out of-pocket spending in a country for health care increased between 2003 and 2008. The function f(x) = 2574e^(0.0359x) models average annual expenditures per household, in dollars. In this model, x represents the year, where x = 0 corresponds to 2003.

(a) Estimate out-of-pocket household spending on health care in 2008.

(b) Determine the year when spending reached $2875 per household

The explanation to the answer is now given as follows:

(a) Estimate out-of-pocket household spending on health care in 2008.

Given;

f(x) = 2574e^(0.0359x) ........................ (1)

Since x = 0 corresponds to 2003; by counting from 2003 to 2008, it implies that x = 5 corresponds to 2008.

Substituting x = 5 into equation (1) to estimate out-of-pocket household spending on health care in 2008, we have:

f(6) = 2574e^(0.0359 * 5)

f(6) = 2574 * 1.19661890406748

f(6) = 3,080.09705906969

Rounding to the nearest dollar as needed, we have:

f(6) = $3,080

Therefore, the total expenditures per household in the year 2008 were approximately $3,080.

(b) Determine the year when spending reached $2875 per household

This can be determined using equation (1) in part a by equating f(x) to $2875 solve for x as follows:

2875 = 2574e^(0.0359x)

2875 /2574 = e^(0.0359x)

1.11693861693862 = e^(0.0359x)

Taking the natural log of both sides, we have:

ln(1.11693861693862) = ln(e^(0.0359x))

0.110591565075382 = 0.0359x

x = 0.110591565075382 / 0.0359

x = 3.0805449881722

Approximating to a whole number, we have:

x = 3

Since x = 0 corresponds to 2003; by counting from 2003, x = 3 corresponds to 2006.

Therefore, the spending reached $2875 per household in 2006.

An exponential model can be found when two data points from the model are known.

The total expenditures per household in the year 2008 were near $3,080.

The spending reached $2875 per household in year 2006

(a). Out of-pocket spending in a country for health care given by function,         [tex]f(x) = 2574e^{0.0359x}[/tex]

Since [tex]x = 0[/tex] corresponds to 2003, Similarly, x = 5 corresponds to 2008.

Substituting x = 5 into above function to estimate out-of-pocket household spending on health care in 2008

[tex]f(5) = 2574e^{0.0359*5} \\\\f(5)=3080[/tex]

f(5) = $3,080

Therefore, the total expenditures per household in the year 2008 were approximately $3,080.

(b). To determine the year when spending reached $2875 per household

 [tex]2875 = 2574e^{0.0359x} \\\\2875/2574=e^{0.0359x} \\\\1.1169=e^{0.0359x}[/tex]

 Taking natural log on both side

[tex]x=\frac{ln(1.1169)}{0.0359} =3.07[/tex]

Since x = 0 corresponds to 2003, So  x = 3 corresponds to 2006.

Therefore, the spending reached $2875 per household in 2006.

Learn more:

https://brainly.com/question/12375190

plz help me thanks so mycghh​

4,408,703 in expanded form.

¿Cuál es el área del siguiente polígono regular 12 lados que mide 6cm de lado y tiene una apotema de 5.2cm? *

HHURRY BEING TIMED read this from a story walk around the pyamids and through the wo
pathenon hight on a hill catches the first light of morning the the carvers wanted the sight of that golden light wasing across the hourse and a line of other gods to be inforgettable and so they coaxed the images of their gods out of the marble with suc treness of there gods out of marble

which important detail does the phhotograph best help readers understand

A ; EACH figure is a clam and as refined as our mind can imagine

B; THE SIGHT OF THAT GOLDEN LIGHT WASHING ACROSS THE HOURES AND
A LINE OF OTHER GODS TO BE UNFORGETTABLE .

C pathenon high on a hill catches the first light of morning

D they gave the world an example of ideal beauty

NOT PLS NOT GUSS

A card is drawn at random from a standard 52-card deck. What is the probability of drawing a red card or a 7 of spades?

____2. Find the value of x

A 16 C 50
B 34 D 70

Help please!!!!!!!!!

SOMEONE HELP ME ASAP PLEASEE

I've hit multiple kids with my Truck

Turn the sentence into an expression please

9. twenty more than a number added to the
difference between the number and nine

A coffee shop sells 4 types of coffee, 10 types of tea, and 5 sodas. How many different types of drinks does the coffee shop sell?

12. Complete the two-column proof.
Given: m 22 m23
Prove: m21-m24
Statements
Reasons
1. m 2 = m23
1.
Given
2.
2. m2 1 + m22 = 180°
m23 + 24 = 180°
3. m2 1 + m2 = m23 + m24
3.
4. m21 = 24
4.

2 Why is adding 6, 10, and 5 to a number the same as
adding 21 to that number?

Seven
Cruel
Hours
Of
Our
Lifes


what math means
Mental
Abuse
To
Humans

Help me pleaseeeeeeeeeeeeeeeeeee

McKayla hikes 8 miles on Monday. On Tuesday she
hikes 30% more miles than on Monday. What is the
NEW AMOUNT of miles she hikes on Tuesday?

(GIVING BRAINLIEST & EXTRA POINTS!! PLS DRAW IT OUT! I DONT WANT TO KNOW THE ANSWER TO THE MULTIPLICATION, I WANT TO SEE HOW YOU SOLVE IT TO GET THE ANSWER :))




1. Use the square grid to find the area.

4 cm x 1 41 cm =_________



Here is the image:

What is the slope-intercept form of the linear equation 2x–8y=32?

For 0° ≤ x < 360°, what are the solutions to sin(StartFraction x Over 2 EndFraction) + cos(x) – 1 = 0 ?

{30°, 150°}
{60°, 300°}
{120°, 240°}
{210°, 330°}

Which exponential function has an x-intercept?
A.
F(x) = 100+-5-1
B.
F(x) = 3x4+2
C.F(x) = 7+-1 + 1
D.
F(x) = -8x+1 – 3

Which of the following option(s) is a unique curve that can be defined using polar coordinates? Select all that apply.

Rose
rational expression
cardioid
cubic function
lemicon

x=2y-6;y=3x-7
substitution to solve systems of equations​

Jeffery bought 203 sheets of stickers. Each sheet has a dozen stickers. He gave away 907 stickers to his family on Valentine's Day. How many stickers does Jeffery have remaining?

Are the ratios 6:5 and 4:3 equivalent?​

Please help me don’t do it for points

y = cos 4(x) period
​

A car travels 351 miles on 13 gallons of gas. What is the number of miles driven per gallon of gas?

a. 24 mpg
b.27 mpg
c. 29 mpg
d. 28 mpg

Which of the following exponential functions goes through the points (1, 20) and (2, 80)?
O f(x) = 5(4)-
O f(x) = 4(5)-*
O f(x) = 5(4)*
O f(x) = 4(5)*

Question 3 (2 points)
A unit rate is
A rate in which the second quantity in the comparison is one unit.

One-third of the result of three times a number that is increased by 12