1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
stiv31 [10]
3 years ago
5

According to data from a medical​ association, the rate of change in the number of hospital outpatient​ visits, in​ millions, in

a certain country each year from 1980 to the present can be approximated by f’(t) = 0.001155t(t-1980)^0.50, where t is the year.
a. Using the fact that in 1980 there were 264,034,000 outpatient​ visits, find a formula giving the approximate number of outpatient visits as a function of time.
b. Use the answer to part a to forecast the number of outpatient visits in the year 2015.
Mathematics
1 answer:
GaryK [48]3 years ago
3 0

Answer:

a) f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000

b) f(t=2015) = 264,034,317.7

Step-by-step explanation:

The rate of change in the number of hospital outpatient​ visits, in​ millions, is given by:

f'(t)=0.001155t(t-1980)^{0.5}

a) To find the function f(t) you integrate f(t):

\int \frac{df(t)}{dt}dt=f(t)=\int [0.001155t(t-1980)^{0.5}]dt

To solve the integral you use:

\int udv=uv-\int vdu\\\\u=t\\\\du=dt\\\\dv=(t-1980)^{1/2}dt\\\\v=\frac{2}{3}(t-1980)^{3/2}

Next, you replace in the integral:

\int t(t-1980)^{1/2}=t(\frac{2}{3}(t-1980)^{3/2})- \frac{2}{3}\int(t-1980)^{3/2}dt\\\\= \frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}+C

Then, the function f(t) is:

f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+C'

The value of C' is deduced by the information of the exercise. For t=0 there were 264,034,000 outpatient​ visits.

Hence C' = 264,034,000

The function is:

f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000

b) For t = 2015 you have:

f(t=2015)=0.001155[\frac{2}{3}(2015)(2015-1980)^{1/2}-\frac{4}{15}(2015-1980)^{5/2}]+264,034,000\\\\f(t=2015)=264,034,317.7

You might be interested in
What is the first day of spring
nasty-shy [4]

Answer:

The first day of spring is  Thursday, March 19th.

The first day of summer is June 20th. So, Spring ends on June 20th.

Step-by-step explanation:

<em>I looked it up on the internet instead of asking on brainly.</em>

8 0
3 years ago
Read 2 more answers
Select the statement which best fits the justification for the step in Line 5.
zvonat [6]

Do you know the answer???


4 0
3 years ago
Read 2 more answers
Marco drew 24 he drew 1/6 of them in art class how many pictures did Marco draw in class
anzhelika [568]
24×1/6 =24/6 = 4

Marco drew 4 pictures
5 0
3 years ago
Laura checked her outdoor thermometer and noticed that the temperature rose from 31 degrees in the morning to 45 degrees in the
harina [27]
The temperature increases by 45% so far.
4 0
3 years ago
Read 2 more answers
A househusband is cooking beef stew for his family in a pan that is (a) uncovered, (b) covered with a light lid, and (c) covered
raketka [301]

Answer:

Cooking will be shortest when the househusband covers the beef stew with the heavy lid.

Step-by-step explanation:

The explanation for this is that water boils at 100°C at normal atmospheric pressure & it remains at that temperature until all the water evaporates as steam; the temperature can then go higher in steam form.

So, if he leaves the pan uncovered the pressure above the beef stew will be the atmospheric pressure and the temperature of the stew will not pass the 100°C mark and the food cooks at 100°C.

If he places a light lid on top, the pressure will build up & the temperature at which water remains liquid is a bit higher, but eventually the steam will push the lid to escape thereby releasing pressure & reducing the temperature.

If he puts a heavy lid on the pan the pressure can build up the highest and the temperature of the water in the stew will stay the highest ensuring the fastest cooking.

Basically, the heavier the lid, greater the pressure in the pan. As the pressure gets greater, the saturation temperature at which water starts boiling will be higher. And higher boiling temperatures mean shorter cooking times.

8 0
3 years ago
Other questions:
  • What is the value of x in the equation −6 + x = −1? (10 points)
    12·2 answers
  • ???????????????????????
    15·1 answer
  • HELP HELP HELP PLEASE HELP!!!!!!!!!!!!!! I NEED HELP!!!!!!!!!!!!!!!!!! I need this question answered ASAP!!! I need my grade to
    5·1 answer
  • If a car can travel 435 miles on 25 gallons of gas how many miles per gallon does the car get?
    13·1 answer
  • What’s the slope ? I don’t understand
    8·1 answer
  • What you get when you add numbers together
    9·1 answer
  • A baseball training clinic takes out a loan to build a new reception area. The loan is for $28,500 at 4.25% for five years. How
    10·1 answer
  • When an object accelerates, it changes its
    7·1 answer
  • I need help on this and the first person who answer correctly gets a BRANILIST​
    15·1 answer
  • Pls pls pls pls pls help me out​
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!