![ellamai16](/avatars/23562.jpg)
ellamai16
26.08.2019 •
Mathematics
This is a homeork problem from my class
"the life expectancy for females born during 1980-1985 was aproximately 77.6 years. this grew to 78 years during 1985-1990 and to 78.6 years during 1990-1995. construct a model for this data by finding a quadratic function whose graph passes through the points (0,77.6), (5,78), and (10,78.6). use this model to estimate the life expectancy for females born between 1995 and 2000 and for those born between 2000 and 2005."
must show all work and use elimination method
Solved
Show answers
More tips
- F Food and Cooking How to Cook Julienne? Recipes and Tips...
- D Dating, Love, Relationships 10 Useful Tips on How to Survive a Breakup?...
- F Food and Cooking Apple Cider Vinegar: The Ultimate Health and Beauty Solution...
- C Computers and Internet Е-head: How it Simplifies Life for Users?...
- F Family and Home How to Choose the Best Diapers for Your Baby?...
- F Family and Home Parquet or laminate, which is better?...
- L Leisure and Entertainment How to Properly Wind Fishing Line onto a Reel?...
- L Leisure and Entertainment How to Make a Paper Boat in Simple Steps...
- T Travel and tourism Maldives Adventures: What is the Best Season to Visit the Luxurious Beaches?...
- H Health and Medicine Kinesiology: What is it and How Does it Work?...
Answers on questions: Mathematics
- M Mathematics Pls answer :( I’ll appreciate!...
- M Mathematics I have no idea what to do here please help...
- M Mathematics Write the first 4 terms of the sequence. f(1) = 2 and f(n) = f(n - 1) + 2 for each whole number n greater than 1. A 1,3,5, 7 B) 2,4,6,8 C) 1,2,3,4 D) 2,3,4,5 How...
- M Mathematics Omar s test score average decreased by 6 points this semester. Write a signed number to represent this change in average....
- M Mathematics Anna walked 1/8 of a mile in 1/16 of an hour what was her walking speed in miles per hour...
- M Mathematics The entrance fee at Purple Dinosaur Carnival was $4.00, and each ride cost $0.80. The entrance fee at Unicorn Carnival was $12.00, and each ride cost $0.30. If...
- M Mathematics Write an expression to find the difference in the maximum area and minimum area of NYSE high school soccer field...
- M Mathematics 1/12 Multiply (3v – 8)(v +6) A) 312 – 26V + 48 C) 3v2 + 101 - 48 B) 30v2 - 41 - 48 D) 312 - 48...
- M Mathematics at the beginning of the basketball game Sabrina made nine points in four minutes she wants to break the school record of 119 points in a game but the game last...
- M Mathematics What is the range set of E = {(3, 3), (4, 4), (5, 5), (6, 6)}...
Ответ:
To solve this problem we have to use the quadratic function. An equation where the highest exponent is (usually "x") is a square (2).
Quadratic function = f(x)=ax²+bx+c
Three points have been given to us
⇒ (0 , 77.6)
⇒ (5 , 78)
⇒ (10 , 78.6)
Calculations
(0 , 77.6)
x=0
f(x)=77.6
a(0)²+b(0)+c=77.6
c=77.6
(5 , 78)
a(5)²+b(5)+77.6=78
25a+5b=78-77.6
25a+5b=0.4 (1)
(10 , 78.6)
a(10)²+b(10)+77.6=78.6
100a+10b=78.6-77.6
100a+10b=1 (2)
As you see equations number (1) and (2) have a system
100a+10b=1
25a + 5b=0.4
We solve this system we have to use elimination. In the elimination method you can add or subtract the equations to get an equation into one variable.
100a+10b=1
-4(25a+5b=0.4)
≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
-10b=-0.6
⇒ b=-0.6/-10=0.06
100a+10b=1
-2(25a+5b=0.4)
≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
50a = 0.2
⇒ a=0.2/50=0.004
Now we have a, b and c:
α = 0.004
β = 0.06
c = 77.6
Therefore, the quadratic function is:
f(x)=0.004x²+0.06x+77.6
x=year of the beginning of the interval - 1980
The life expectancy for females born between 1995 and 2000 is when
x=1995-1980=15
Therefore we do
f(15)=0.004(15)²+0.06(15)+77.6
f(15)=0.004(225)+0.06(15)+77.6
f(15)=79.4
Females between 2000 and 2005
x=2000-1980=20
Now we do
f(20)=0.004(20)²+0.06(20)+77.6
f(20)=1.6+1.2+77.6
f(20)=80.4
The life expectancy for females born between 1995 and 2000 = 79.4 years.
The life expectancy for females born between 2000 and 2005 = 80.4 years.
Ответ:
f(x)=ax²+bx+c
We have three points:
(0 , 77.6)
(5 , 78)
(10 , 78.6)
Then, we make the function wiht these points:
(0 , 77.6)
x=0
f(x)=77.6
a(0)²+b(0)+c=77.6
c=77.6
(5 , 78)
a(5)²+b(5)+77.6=78
25a+5b=78-77.6
25a+5b=0.4 (1)
(10 , 78.6)
a(10)²+b(10)+77.6=78.6
100a+10b=78.6-77.6
100a+10b=1 (2)
With the equations (1) and (2) we have a system of equations:
100a+10b=1
25a + 5b=0.4
We solve this system of equations by method of elimination.
100a+10b=1
-4(25a+5b=0.4)
-10b=-0.6 ⇒ b=-0.6/-10=0.06
100a+10b=1
-2(25a+5b=0.4)
50a = 0.2 ⇒ a=0.2/50=0.004
We have a, b and c:
a=0.004
b=0.06
c=77.6
Therefore, the quadratic funtion is:
f(x)=0.004x²+0.06x+77.6
x=year of the beginning of the interval - 1980
The life expectancy for females born between 1995 and 2000 is when x=1995-1980=15
Therefore:
f(15)=0.004(15)²+0.06(15)+77.6
f(15)=0.004(225)+0.06(15)+77.6
f(15)=79.4
The life expectancy for females born between 2000 and 2005 is when:
x=2000-1980=20
therefore:
f(20)=0.004(20)²+0.06(20)+77.6
f(20)=1.6+1.2+77.6
f(20)=80.4
The funtion is:
f(x)=0.004x²+0.06x+77.6
x=year of the beginning of the interval - 1980
The life expectancy for females born between 1995 and 2000 is 79.4 years.
The life expectancy for females born between 2000 and 2005 is 80.4 years.
Ответ:
k<4
Hope that helps!