Answer:
Part A)
About 0.51% per year.
Part B)
About 0.30% per year.
Part C)
About 28.26%.
Step-by-step explanation:
We are given that the population of Americans age 55 and older as a percentange of the total population is approximated by the function:
[tex]f(t) = 10.72(0.9t+10)^{0.3}\text{ where } 0 \leq t \leq 20[/tex]
Where t is measured in years with t = 0 being the year 2000.
Part A)
Recall that the rate of change of a function at a point is given by its derivative. Thus, find the derivative of our function:
[tex]\displaystyle f'(t) = \frac{d}{dt} \left[ 10.72\left(0.9t+10\right)^{0.3}\right][/tex]
Rewrite:
[tex]\displaystyle f'(t) = 10.72\frac{d}{dt} \left[(0.9t+10)^{0.3}\right][/tex]
We can use the chain rule. Recall that:
[tex]\displaystyle \frac{d}{dx} [u(v(x))] = u'(v(x)) \cdot v'(x)[/tex]
Let:
[tex]\displaystyle u(t) = t^{0.3}\text{ and } v(t) = 0.9t+10 \text{ (so } u(v(t)) = (0.9t+10)^{0.3}\text{)}[/tex]
Then from the Power Rule:
[tex]\displaystyle u'(t) = 0.3t^{-0.7}\text{ and } v'(t) = 0.9[/tex]
Thus:
[tex]\displaystyle \frac{d}{dt}\left[(0.9t+10)^{0.3}\right]= 0.3(0.9t+10)^{-0.7}\cdot 0.9[/tex]
Substitute:
[tex]\displaystyle f'(t) = 10.72\left( 0.3(0.9t+10)^{-0.7}\cdot 0.9 \right)[/tex]
And simplify:
[tex]\displaystyle f'(t) = 2.8944(0.9t+10)^{-0.7}[/tex]
For 2002, t = 2. Then the rate at which the percentage is changing will be:
[tex]\displaystyle f'(2) = 2.8944(0.9(2)+10)^{-0.7} = 0.5143...\approx 0.51[/tex]
Contextually, this means the percentage is increasing by about 0.51% per year.
Part B)
Evaluate f'(t) when t = 17. This yields:
[tex]\displaystyle f'(17) = 2.8944(0.9(17)+10)^{-0.7} =0.3015...\approx 0.30[/tex]
Contextually, this means the percetange is increasing by about 0.30% per year.
Part C)
For this question, we will simply use the original function since it outputs the percentage of the American population 55 and older. Thus, evaluate f(t) when t = 17:
[tex]\displaystyle f(17) = 10.72(0.9(17)+10)^{0.3}=28.2573...\approx 28.26[/tex]
So, about 28.26% of the American population in 2017 are age 55 and older.
Two pieces of equipment were purchased for a total of $5000. If one piece cost $410 more than the other, find the price of the less expensive piece of equipment
Answer:
correct answer explained above
The graph show how many minutes it takes Ziah to run a certain distance in the city What is the constant of proportionality? Write your answer as a decimal
need answer in 5 minutes will give brainliest
Explanation:
The constant of proportionality is the same as the slope for equations of the form y = kx.
To find the value of k, we divide the y over x values.
k = y/x = 12/8 = 1.5
or
k = y/x = 6/4 = 1.5
Either way the answer is 1.5
This means Ziah ran at a rate of 1.5 city blocks per minute.
Casey borrowed $4500 at a 5% interest rate for 4 years.
What was the total interest?
Enter your answer in the box.
Hint: Use the formula l=P*R*T where
I= Interest Earned/Owed
P= Principal
R= Rate
T= Time
Answer:
$900
Step-by-step explanation:
Put the numbers in the formula and do the arithmetic.
I = PRT
I = ($4500)(0.05)(4) = $900
The total interest was $900.
[tex]\large\tt\green{Answer}[/tex]
The total interest was $900[tex]\large\tt\green{Step-by-step \: explanation}[/tex]
Step 1:
Put the numbers in the formula and do the arithmetic.
I = P × R × TI = $4500 × 5% × 4Step 2:
Rename 5% into decimal
I = P × R × TI = $4500 × 0.05 × 4Step 3:
Solve the problem with the full solution.
I = P × R × TI = $4500 × 5% × 4I = $4500 × 0.05 × 4I = $ 900Therefore, the total interest was $900
5.4-0.25 I'm so confused
Answer:
5.15
Step-by-step explanation:
Answer:
5.15
Step-by-step explanation:
5.4 = 5.40
5.40
- 0.25
= 5.15
because 0.40 - 0.25 = 0.15
Can someone help me please
Answer:
31.25
Step-by-step explanation:
Divide 250 by 8=31.25
Sally was standing 30 feet from a tree.The angle of elevation from her eyes(standing 4 feet above the ground) to the top of the tree was 38. How tall is the tree? Round your answer to the nearest foot
Answer:
27ft-long
Step-by-step explanation:
good luck!!!
Please help! I need help with this question.
Answer:
check online for more information
Miriam has 3 packages of pencils. Each
package has 6 pencils. She needs an
eraser for each pencil. How many erasers
will she need to buy?
Tell which OPERATIONS you will use. Then
solve the problem. (Very important).
Answer:
18
Step-by-step explanation:
you will use multiplication
3(packages of pencils)×6(pencils)=18pencils
so she will need 18 erasers for each pencil
whats the answer to 3 1/2 divided by 2 1/4
Answer:
1.556
Step-by-step explanation:
Divide
3 and 1 over 23
1
2
÷ 2 and 1 over 42
1
4
= 28 over 18
28
18
Step 1 of 2: Divide, sub-step a: Convert mixed number to improper fraction.
Convert mixed number to improper fraction
3 and 1 over 23
1
2
= ( 3 × 2 ) over 2
3 × 2
2
+ 1 over 2
1
2
= ( 6 + 1 ) over 2
6 + 1
2
= 7 over 2
7
2
Step 1 of 2: Divide, sub-step b: Convert mixed number to improper fraction.
Convert mixed number to improper fraction
2 and 1 over 42
1
4
= ( 2 × 4 ) over 4
2 × 4
4
+ 1 over 4
1
4
= ( 8 + 1 ) over 4
8 + 1
4
= 9 over 4
9
4
Step 1 of 2: Divide, sub-step c: Divide.
Divide
7 over 2
7
2
÷ 9 over 4
9
4
= 7 over 2
7
2
× 4 over 9
4
9
= ( 7 × 4 ) over ( 2 × 9 )
7 × 4
2 × 9
= 28 over 18
28
18
To divide fractions, invert the second one (turn it upside-down), then multiply the numerators and denominators.
Step 1 of 2: Divide.Hide
Step 2 of 2: Simplify.
Simplify
28 over 18
28
18
= 14 over 9
14
9
= 1 and 5 over 91
5
9
Step 2 of 2: Simplify, sub-step a: Reduce fraction to lowest terms.
Reduce fraction to lowest terms
28 over 18
28
18
= ( 28 ÷ 2 ) over ( 18 ÷ 2 )
28 ÷ 2
18 ÷ 2
= 14 over 9
14
9
2 is the greatest common divisor of 28 and 18. Reduce by dividing both numerator and denominator by 2.
Step 2 of 2: Simplify, sub-step b: Convert improper fraction to mixed number.
Convert improper fraction to mixed number
14 over 9
14
9
= 1 and 5 over 91
5
9
14 ÷ 9 = 1 remainder 5
Answer:
1.5555555555556
Step-by-step explanation:
when you divide those numbers, thats your answer
Hi, I'm going to be starting homeschooling most likely from 7th to 12th Grade mainly due to my Public School failing me miserably and C0vid. I was curious if anyone could recommend me any home-schooling programs? All I'm looking for in a home-school is one that's easy in math or one that potentially has a lot of multiple-choice questions as obviously i will be using this website a lot to help me get through the stuff i don't exactly fully understand. All replies are GREATLY appreciated, Thank you so much.
Answer:
I use connexus :)
Step-by-step explanation:
emma is finding 7/2 x 2/5
Answer:
14/10
OR
7/5
Step-by-step explanation:
(7*2)/(2*5) = 14/10
(14/2) / (10/2) = 7/5
Answer:
Mixed fraction: 1 2/5
Decimal form: 1.4
Hope this helps :)
7 1/4 -3 3/4= 4 1 /4 - 3/4
Answer:
7/2
Step-by-step explanation:
The length of a man's shadow is directly proportional with his height.
At the same time of day, a man who is 1.8 meters tall casts a 25.2
meter shadow and his son casts a 21 meter shadow. What is the
height of the man's son, in meters? If necessary, round to the nearest
tenth.
Answer:
The man's son height is 1.5m
Step-by-step explanation:
[tex]\frac{x}{21} =\frac{1.8}{25.2}[/tex]
[tex]\frac{21x1.8}{25.2}[/tex]
21x1.8= 37.8
37.8 ÷ 25.2= 1.5
Hope this helps
sorry if i got it wrong
find the equation of a circle (3,2) (1,4)
Answer:
y = −x + 5
Explanation:
Use the slope formula and slope-intercept form y = mx + b to find the equation.
Hope this helped. Have a good one!
What is 1 + 1 I need to know.
Answer:
2
Step-by-step explanation:
please mark my answer in brainlist
Answer:
2
Step-by-step explanation:
1+1=2
How to graph the table
Kripa’s father is 35 years younger than her grandfather, and 40 years older than her. If the sum of the ages of the three is 160 years, let’s find her grandfather’s age?
Answer:
90 years
Step-by-step explanation:
if Kripa's age = x
Father's age = x + 40
Grandfather's age = (x + 40) + 35 = x + 75 (father is 35 years younger than grandfather i.e. grandfather is 35 years older than father)
x + x + 40 + x + 75 = 160
=> 3x = 160 - 115
=> x = 45/3 = 15
grandfather's age = x + 75 = 90 years
Answer:
90 yearsStep-by-step explanation:
x + x + 40 + x + 75 = 160
=> 3x = 160 - 115
=> x = 45/3 = 15
Grandfather's age = x + 75 = 90 years
You plant 9 rows of different bulbs in a garden. For each row, you use the rule, “onion, onion, garlic, flower.” How many garlic and flower bulbs do you plant altogether? How many bulbs do you use in all?
Answer:
18; 36
Step-by-step explanation:
If there's 9 rows of "onion, onion, garlic, flower", then you repeat this cycle 9 times.
onion, onion, garlic, flower(1)
onion, onion, garlic, flower(2)
onion, onion, garlic, flower(3)
onion, onion, garlic, flower(4)
onion, onion, garlic, flower(5)
onion, onion, garlic, flower(6)
onion, onion, garlic, flower(7)
onion, onion, garlic, flower(8)
onion, onion, garlic, flower(9)
Add up the garlic and flower bulbs, which equals 18. Then add up all of the bulbs, which is 36.
-hope it helps
A total of 180 students and 35 chaperones are going on a field trip to the Smithsonian Institution in Washington, D. C.
Write the ratio in simplest form.
the ratio of students to people on the trip
Answer:
36 : 43
Step-by-step explanation:
So, we have 180 : 35 + 180 in the students to people on the trip180 : 21536 : 43Therefore, the ratio of students to people is 36 : 43Gemma and Leah are both jewelry makers, Gemma made 106 beaded necklaces. Leah
made 39 more necklaces than Gemma.
Each necklace they make has exactly 104 beads on it. How many beads did both
Jewelers use altogether while making their necklaces? How many necklaces did Gemma and Leah each make
Answer:
Gemma made $34 more than Leah.
Step-by-step explanation:
Gemma made number of beaded necklaces = 106
Leah made 39 more necklaces than Gemma.
Leah made number of beaded necklaces = 106 + 39 = 145
a. There are 104 beads on each necklace.
The total number of beads used altogether
= (106 × 104) + (145 × 104)
= 11,024 + 15,080
= 26,104
b. Gemma sold her 106 necklaces for = $14
Total price of her necklaces = 106 × 14
= $1,484
Leah sold her 145 necklaces for = $10
Total price of her necklaces = 145 × 10
= $1,450
Difference in Gemma and Leah's amount = 1484 - 1450 = $34.00
Therefore, Gemma made $34.00 more money than Leah.
You use a garden hose to fill a wading pool. If the water level rises 16 centimeters every 7 minutes
and you record the data point of (21,y), what is the value of y? Use slope to justify your answer.
The rate of change at which the water level rises is ____ centimeters per minute. So solving the equation ____ for y gives a y-value equal to ____
Which of the following best describes
the slope of the line below?
• A. Positive
• B. Negative
• C. Undefined
D. Zero
Answer:
A. Positive I'm sorry if I got this wrong answer
Answer:
Please add the picture
Step-by-step explanation:
If it point upward right: positive
if it point downward: negative
If it is just a horizontal line : zero
HELPPP FAST LIKE 4 minutes left
Answer: A. 40
Step-by-step explanation:
Solve for x.
5(x−4)2=4x+14
x = 9
x = 8
x=−6
x=−16
Answer:
9 is the answer.
Step-by-step explanation:
5(x − 4)2 = 4x + 14
=> 10x - 40 = 4x + 14
=> 6x = 54
=> x = 9
Therefore, 9 is the answer.
Hoped this helped.
The value of the x after solving the equation 5 (x - 4) 2 = 4x + 14 is x = 9.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Given linear equation,
5 (x - 4) 2 = 4x + 14
5 × 2 (x - 4) = 4x + 14
10 (x - 4) = 4x + 14
By distributive property, p (q + r) = p q + p r
10x - (10 × 4) = 4x + 14
10x - 40 = 4x + 14
10x - 4x = 14 + 40
6x = 54
x = 54 / 6
x = 9
Hence the value of x is 9.
To learn more about Linear Equations, click on the link given below :
https://brainly.com/question/11897796
#SPJ2
which of the following represents an arithmetic sequence with a common difference of -8.5?
Answer:
C
Step-by-step explanation:
to have a common difference of -8.5, the sequence has to consistently go down by 8.5.
in the first one, y would go up by 2 every time x goes up by 1, so its not that one.
in the second one, it does go down by 8.5 the first time but the next time it goes down by 4.25, so it's not consistent.
in the third one, each time it goes down by 8.5 so this is the answer.
the fourth one also isn't correct because the graph shows that it is going up, so you know for sure it's not that one.
Help pls , I’m lost
Use the distributive property to simplify this expression -2x(3x + x-5)
Answer:
− 8 x ^2 + 10 x
Step-by-step explanation:
satellite makes 4 revolutions of the earth in one day. How many revolutions would it make in 6 1/2 days?
3.
Billy and Karen are playing a billy and Karen are playing a game. They toss a coin that can land either heads or tails and a
spinner that can land on any of 8 equal regions. If a coin is tossed and the spinner is spun,
howmany possible outcomes are there?
The number of possible outcomes for both Billy and Karen = 32 possible outcomes.
A coin has head and tail and thus;
Number of possible outcomes of a coin toss = 2
Now, for the for the spinner, since there are 8 equal regions;
The number of possible outcomes of the spinner = 8
Now, since they are playing a game;
Number of possible outcomes for Billy for one toss of coin and one time of spinning the spinner = 8 × 2 = 16
Similarly;
Number of possible outcomes for Karen for one toss of coin and one time of spinning the spinner = 8 × 2 = 16
Therefore;
Total possible outcomes for both Karen and Billy = 16 + 16 = 32 possible outcomes.
Read more about probability at; https://brainly.com/question/21186493
WILL GIVE BRAINLIEST!!!!
Answer:
$319
Step-by-step explanation:
Usually, sales tax is proportional to the amount of the sale, so if the sales tax is a factor of 22/16 times the original tax, then the sale amount must be 22/16 times the original item cost:
(22/16)·$232 = $319
