The function N(t) = 100e^−0.023t models the number of grams in a sample of cesium-137 that remain after t years. On which interval is the sample's average rate of decay the fastest?
Options:
A. [1,10] B. [10,20] C. [15,25] D. [1,30]
Answer:
A. [1,10]
Step-by-step explanation:
Given
[tex]N(t) = 100e^{-0.023t}[/tex]
Required
Interval with the fastest rate of decay
The rate of change over [a,b] is calculated as:
[tex]Rate = \frac{N(b) - N(a)}{b - a}[/tex]
So, we have:
A. [1,10]
[tex]Rate = \frac{N(10)-N(1)}{10 - 1}[/tex]
[tex]Rate = \frac{N(10)-N(1)}{9}[/tex]
Calculate N(10) and N(1)
[tex]N(10) = 100e^{-0.023*10} = 100e^{-0.23} = 79.45[/tex]
[tex]N(1) = 100e^{-0.023*1} = 100e^{-0.023} = 97.73[/tex]
So:
[tex]Rate = \frac{79.45-97.73}{9} = \frac{-18.28}{9} = -2.03[/tex]
B. [10,20]
[tex]Rate = \frac{N(20)-N(10)}{20 - 10}[/tex]
[tex]Rate = \frac{N(20)-N(10)}{10}[/tex]
Calculate N(20) and N(10)
[tex]N(20) = 100e^{-0.023*20} = 100e^{-0.46} = 63.13[/tex]
[tex]N(10) = 100e^{-0.023*10} = 100e^{-0.23} = 79.45[/tex]
So:
[tex]Rate = \frac{63.13 - 79.45}{10} = \frac{-16.32}{10} = -1.632[/tex]
C. [15,25]
[tex]Rate = \frac{N(25)-N(15)}{25 - 15}[/tex]
[tex]Rate = \frac{N(25)-N(15)}{20}[/tex]
Calculate N(25) and N(15)
[tex]N(25) = 100e^{-0.023*25} = 100e^{-0.575} = 56.27[/tex]
[tex]N(15) = 100e^{-0.023*15} = 100e^{-0.345} = 70.82[/tex]
So:
[tex]Rate = \frac{56.27 - 70.82}{10} = \frac{-14.55}{10} = -1.455[/tex]
D. [1,30]
[tex]Rate = \frac{N(30)-N(1)}{30 - 1}[/tex]
[tex]Rate = \frac{N(30)-N(1)}{29}[/tex]
Calculate N(30) and N(1)
[tex]N(30) = 100e^{-0.023*30} = 100e^{-0.69} = 50.16[/tex]
[tex]N(1) = 100e^{-0.023*1} = 100e^{-0.023} = 97.73[/tex]
So:
[tex]Rate = \frac{50.16 - 97.73}{29} = \frac{-47.57}{29} = -1.64[/tex]
By comparing the values of the calculated rates,
-2.03 is the smallest, in other words; the fastest rate
Hence, the interval [1,10] has the fastest rate of decay
The required average rate of change is the fastest on [tex][1,10][/tex].
The average rate of change :The formula for the average rate of change on the interval [tex][a,b][/tex] is,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{b-a}[/tex]
Now, applying the given function into the above function is,
Now, [tex]a=1,b=10[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{10-1} =-2.03[/tex]
Now, [tex]a=10,b=20[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{20-10} =-1.6325[/tex]
Now, [tex]a=15,b=25[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{25-15} =-1.455[/tex]
Now, [tex]a=1,b=30[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{30-1} =-1.64[/tex]
So the average rate of change is fastest on [tex][1,10][/tex]
Learn more about the topic of the average rate of change:
https://brainly.com/question/20884505
There are two bags containing only purple and yellow marbles. Bag A has yellow marbles and purple marbles. Bag B has yellow marbles and purple marbles. A marble is randomly chosen from each bag. List these events from least likely to most likely. Event : choosing a purple marble from Bag B. Event : choosing a yellow or purple marble from Bag A. Event : choosing a red marble from Bag B. Event : choosing a yellow marble from Bag A.
the principal likes to keep the ratio of students to teachers at 24:1 if he has hired 32 teachers then how many students are expected to enroll
Answer:
768 students are expected to enroll
Step-by-step explanation:
24 : 1
? : 32
24 times 32 = 768
esme takes the bus to university 40 times during a term to relative frequency of the bus being late is 0.3
how many times is the bus late ?
Answer:
I Don't know....
Step-by-step explanation:
sry.....
Answer: 12
Step-by-step explanation:
So.
40 multiplied by 0.3 is 12
Greg rented a truck for one day. There was a base fee of $15.95, and there was an additional charge of 85 cents for each mile driven Grey had to pay $159.57
when he returned the truck For how many miles dhe drive the truck
Answer:
168.964706 miles
Step-by-step explanation:
Turn the info into a equation: 159.57 = .85x + 15.95
Solve for x (miles)
159.57 = .85x + 15.95
143.62 = .85x
x = 168.964706
can guys help me please
Answer:
there is 243.84 cm in 8 feet
round to the nearest hundredths =3266.53
Are the ratios 4:18 and 2:9 equivalent?
yes
no
Answer:
yes
Step-by-step explanation:
Step-by-step explanation:
Two ratios are given to us and we need to tell whether they are equivalent or not . Firstly let us say we have two ratios q:p and r:s . Here p & q are co-primes and r & s are also co-primes. Then the two ratios will be equal if and only if
q = rp = s .Theefore , the Ratios are ,
[tex]\begin{cases}\tt 4 : 18 \\\tt 2:9 \end{cases}[/tex]
Here we see that the ratio 2:9 is in simplest form that is HCF of 2 & 9 is 1 . But here 4:18 is not in simplest form . HCF of 4 & 18 is not 1 it's 2 .On dividing numerator and denominator by 2 , we have ,
[tex]\tt= \dfrac{4}{18}\\\\ = \tt \dfrac{4 \div 2}{18\div 2}\\\\ = \boxed{\orange{\tt \dfrac{2}{9}}}[/tex]
Therefore since the Ratios are equal in the simplest form . Therefore the Ratios are equal.
Make “a” the subject of the following formula
y + az = z
Sally has a car that accelerates at 5 m/s^2. If the car has a mass of 1000 kg, how much force does the car produce?
F=______
m=______
a=______
Answer:
You have to use the equation F=ma.
F: the force an object has (in this case the unknown)
M: the mass an object has (in this case 1000kg)
A: the acceleration an object has (in this case 5m/s^2)
when you plug in everything you should get F=5000N
Answer:
The answer is 5000 N (Newtons).
Explanation:
F=M*A
F=1000 kilograms * 5 m/s squared
F=5000 Newtons
What is the product of 5.2 x 10^4 and 1.3 x 10^-2?
a. 6.76×10^8
b. 6.76×10^2
c. 6.76×10^-2
d. 6.76×10^-8
Answer:
B is the answer.
6.76×10^2
OMG PLEASE HELP YOUR BOY OUT I NEED TO GET THIS ONE RIGHT TO PASS THE TEST!!!
Which of the following rational functions is graphed below?
A. F(x) = (x - 1)/((x + 2) ^ 2)
B. F(x) = (x + 1)/((x + 3)(x - 2))
C. F(x) = (x - 1)/(x(x - 3))
D. F(x) = (x - 1)/(x(x + 2)) O
Answer:
The Answer is C
Write the equation of the line shown in the graph below
Can someone please help both of these
Answer:
4x/3-2
-x/2 +5
this are the answers
Brandon just bought a new coffee table. The length of the coffee table is 5 more than 3 times the width. If the perimeter of the coffee table top is 58 inches, what is the length and width of the coffee table?
Answer:
The length is 23 inches and the width is 6 inches.
Step-by-step explanation:
The perimeter for a rectangular shape is represented as:
P = 2L + 2W, where L represents length and W represents width
We can represent the length as:
L = 3W + 5
Substituting this into the perimeter function, we get:
P = 2 (3W + 5) + 2W
Substituting 58 for P, we get:
58 = 2 (3W + 5) + 2W
58 = 6W + 10 + 2W
58 = 8W + 10
58 - 10 = 8W + 10 - 10
48 = 8W
48 / 8 = 8W / 8
6 = W
With 6 being the established value for the width, we can substitute this back into the equation for length:
L = 3W + 5
L = 3(6) + 5
L = 18 + 5
L = 23
To check our work, we can substitute both the width and length into the perimeter equation:
P = 2L + 2W
58 = 2(23) + 2(6)
58 = 46 + 12
58 = 58
Therefore, length is 23 inches and the width is 6 inches.
Giving brainliest for the correct answer
Answer:
72 is the surface area
SA=2lw+2lh+2hw
l=6
w=3
h=2
please help me. i will give give brainlist. and i will give 5 stars. links will be reported. please follow the directions on the page.
Answer: Graph is not possible here, but i can say plotting point
for first equation (0,3) (2,4) (4,10)
for second equation ( 0,-3) ( 2,-4) (4,-10) plot yourself
Step-by-step explanation:
Work out the size of angle A.
A
11 cm
9 cm
38°
B
С
Student A starts with $100 in the bank and makes $5 a day. Student B starts with $50 and makes $7 a day. Assuming the students save their money, when will they have the same amount of money ?
Answer:
No. They will not have the same amount of money.
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 3.875/100
r = 0.03875 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 10,000.00(1 + 0.03875/12)(12)(7.5)
A = 10,000.00(1 + 0.003229167)(90)
A = $13,366.37
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $10,000.00 at a rate of 3.875% per year compounded 12 times per year over 7.5 years is $13,366.37. Therefore, they cannnot save the same amount.
If a coin and a is die is rolled at same time how many outcomes are possible? Please help me
Answer:
Answer:
12
Step-by-step explanation:
a coin has two possibilities: Head and Tales
a die has six possibilities: 1, 2, 3, 4, 5, 6
2x6=12
Charles inherited $500,000 from his grandfather. He decides to invest the money into a fund that has 4% annual interest. If the interest is compounded continuously, what is the total amount that is compounded annually?
Answer:
this is answer$10,000$1o,5oo ok
Find an expression for the area of the rectangle. Write your answer in standard form.
Answer:
B. 8x² + 18x - 5
Step-by-step explanation:
(2x + 5)(4x - 1)
Use the distributive property to multiply 2x + 5 by 4x - 1.
8x² - 2x + 5(4x) + 5(-1)
8x² - 2x + 20x - 5
Combine 20x and -2x to get 18x.
8x² + 18x - 5
The expression for the area of the rectangle is 8x² + 18x - 5, which is B.
What is the answer to the problem 4x + 6x
Answer:
10x lmboooo
Step-by-step explanation:
combine like terms
Answer:
10x.
Why? Well because 4 + 6 = 10. And since they both are x values the sum is 10x.
Step-by-step explanation:
Hope that this helps! :)
Have great rest of your day/night!
what’s the area besties?
Answer:
36
Step-by-step explanation:
2(4.5*3)=13.5
2(3+7.5)=22.5
13.5+22.5=36
Can you please help me
nvm there is the right answer
5x-4<4(1+x) what is the answer and how do you do it
Answer:
Step-by-step explanation:
5x-4<4(1+x)
5x-4<4+4x
5x-4x<4+4
x<8
f(x) = 3x - 5 for x < -5
f(x) = 5 for 5 < x < 4 4
f(x) = -2x + 5 for 4 < x
piecewise function
Enter the equation of the circle with the given center and radius.
Center: (9, 0)
radius: √5
Answer:
(x - 9)² + y² = (√5)² = 5
Step-by-step explanation:
Start with the standard equation of a circle with center at (h, k) and radius r:
(x - h)^2 + (y - y)^2 = r^2
Now substitute 0 for k, 9 for h and √5 for r:
(x - 9)² + (y - 0)² = (√5)², which simplifies to:
(x - 9)² + y² = (√5)² = 5
Help will mark brainliest no links it trolls. Thx
Answer:
the answer to this question is 22ft
Which point is located at -8.65?
Answer: point b
Step-by-step explanation:
eatch mark on the line is 0.1, b is right behind the 8.6 mark in the middle making it 8.65
Answer:
The answer is point b.
Step-by-step explanation:
The American antelope (pronghorn) and the wildebeest are among the fastest mammals on the planet,
particularly at running long distances. The maximum recorded speed for the antelope is 88.5 km/h, which it
can sustain for nearly one kilometer.
On the other hand, the distance, d, in kilometers that the wildebeest can run in t hours is given by the equation
d=80.5t
Assuming both animals are running at constant speeds, which animal can run faster?
Choose 1 answer:
The American antelope
B
The wildebeest
They can run at the same speed.
Answer:
The Wildebeest
Step-by-step explanation:
I’m guessing
Answer:
Correct answer is a
Step-by-step explanation:
Marissa's work to find the missing
length of the triangle is shown.
Explain Melissa's error.
24 units
az + b2 = c2
102 + 242 = c2
100 + 576 = C2
676 = C2
V676 = 0
338 = C
10 units
Step-by-step explanation:
She has done one mistake at last that under root 676 is not equal to 338, rather it is equal to 26.
Hope it helps ^_^