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3 years ago

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Write H(t) for the amount spent in the United States on health care in year t, where t is measured in years since 2000. The rate

of increase of H(t) was projected to rise from $100 billion per year in 2000 to approximately $190 billion per year in 2010.†(a) Find a linear model for the rate of change H'(t)
H'(t) = ? billion dollars per yr

(b) Given that $1,300 billion was spent on health care in the United States in 2000, find the function H(t).

H(t) = ? billion dollars

1 answer:

Kisachek [45]3 years ago

5 0

Answer:

Check the explanation

Step-by-step explanation:

Write H(t) for the total sum spent in the United States on health care in year t, where t is measured in years since 2000.

The rate of increase of H(t) was projected to rise from $100 billion per year in 2000 to approximately $190 billion per year in 2010

(a) Find a linear model for the rate of change H'(t)

Slope of line is (190-100)/(2010-2000) = 90/10 = 9 billion dollars per yr

H'(t) - 190 = 9 (t-10) =

H'(t) = 9t + 100 billions dollars per year

(b) Given that $1,300 billion was spent on health care in the United States in 2000, find the function H(t).

H'(t) = 9t + 100 billions dollars per year TAKING INTEGRATION..

H(t) = 9t^2/2 + 100t + C given H(0) = 1300

H(0) = 1300 = C

H(t) = 9t^2/2 + 100t + 1300 billion dollars.

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3 years ago

Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 13. Use the empirical rule

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(a) 68% of people has an IQ score between 87 and 113.

(b) 5% of people has an IQ score less than 74 or greater than 126.

(c) 0.15% of people has an IQ score greater than 139.

Step-by-step explanation:

Given information:Scores of an IQ test have a bell-shaped distribution,

mean = 100

standard deviation = 13

According to the empirical rule

68% data lies between $\overline{x}-\sigma$ and $\overline{x}+\sigma$ .

95% data lies between $\overline{x}-2\sigma$ and $\overline{x}+2\sigma$ .

99.7% data lies between $\overline{x}-3\sigma$ and $\overline{x}+3\sigma$ .

(a)

$\overline{x}-\sigma=100-13=87$

$\overline{x}+\sigma=100+13=113$

$[\overline{x}-\sigma,\overline{x}+\sigma]=[87,113]$

Using empirical rule we can say that 68% of people has an IQ score between 87 and 113.

(b)

$\overline{x}-2\sigma=100-2(13)=74$

$\overline{x}+2\sigma=100+2(13)=126$

$[\overline{x}-2\sigma,\overline{x}+2\sigma]=[74,126]$

Using empirical rule we can say that 95% of people has an IQ score between 74 and 126.

The percentage of people has an IQ score less than 74 or greater than 126 is

P = 1- percent of people has an IQ score between 74 and 126.

P = 1- 95%

P = 5%

Therefore 5% of people has an IQ score less than 74 or greater than 126.

(c)

$\overline{x}-3\sigma=100-3(13)=61$

$\overline{x}+3\sigma=100+3(13)=139$

$[\overline{x}-3\sigma,\overline{x}+3\sigma]=[61,139]$

Using empirical rule we can say that 99.7% of people has an IQ score between 61 and 139.

The percentage of people has an IQ score less than 61 or greater than 139 is

P = 1- percent of people has an IQ score between 61 and 139.

P = 1- 99.7%

P = 0.3%

The percentage of people has an IQ score greater than 139 is

$P=\frac{1}{2}(0.3\%)=0.15\%$

Therefore 0.15% of people has an IQ score greater than 139.

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3 years ago