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
Trinity paid $3.50 in tax on a sweatshirt which cost $40. What tax rate does this represent???
kati45 [8]

Answer:

9% tax rate

Step-by-step explanation:

What you do is 3.50/40 and you will get .0875 which will equal

9% tax rate

3 0
3 years ago
What is the largest value in a boxandwhiskers
nevsk [136]
I am pretty sure it is B) upper quartile but not 100% sure
Hope it helps! - Alyssa
3 0
3 years ago
What is the slope of the line that passes through points (-1,5) and (2,-3)
Sonbull [250]

Answer:

-8

Step-by-step explanation:

3 0
3 years ago
How would I solve the equations: y = x-4 and y=x^2-4x using substitution
andriy [413]

Answer:

x = 6

Explanation:

y = x - 4

26 = 4x + y


If y = y, then we can rewrite this system as this: 4x + x - 4 = 26


Then we combine like terms and add 4  on both sides to give us  5  x  =  30 . Divide by 5 on both sides and we arrive at the solution: x = 6

6 0
3 years ago
A fire station is located 2 units to the east and 6 units to the north of a hospital.if the hospital is located at (-2,-3) on a
V125BC [204]
(0,3) because if you go up six on the Y axis you get three. If you go two over on the X axis you reach zero.
7 0
3 years ago
Read 2 more answers
Other questions:
  • Based on what you know about travelogues and Marco Polo's life, what is the best prediction for the purpose of
    12·2 answers
  • Is 13 x 10 ^5 in Scietific Notation? (^ means raised to the power of) Why or why not?
    6·1 answer
  • What is the domain of the function?
    12·2 answers
  • How to find the vertex form of y=-2x^2+4
    9·1 answer
  • Light travels at a speed of about 186,000 miles per second. How far does light travel in 5 second? Use repeated addition to solv
    6·1 answer
  • Please answer for 20 points
    6·2 answers
  • Layla missed 38 questions on her multiple choice math final that had a total of 200
    14·1 answer
  • Ms. Semuskie is buying bagels for her family. How many bagels can she buy for 50$
    13·1 answer
  • A rectangular room measures 15 feet by 18 feet. It is going to be carpeted with carpeting that sells for $38 per square foot.
    15·1 answer
  • What is the volume of the cone in terms of ​π ?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!