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?

Answers

Answer 1

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

Answer 2

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


Related Questions

Find x. Round to the nearest tenth and only type the number for your
answer.
25
X
16
22

Answers

Answer:

10.7

Step-by-step explanation:

To find x we have to basically do pythagoream theorem twice. Both the traingles share the same long side. The find the long side of the top traingle do, [tex]a^{2} +16^{2} =25^{2}[/tex], and we find the long side to be [tex]\sqrt{369}[/tex]. Using this we now plug it into the pythagoream theorem for the bottom triangle. [tex]\sqrt{369} ^{2} +x^{2} =22^{2}[/tex], and doing this out we find that x=[tex]\sqrt{115}[/tex] or about 10.7.

What is the equation of the line that passes through the point (5, -2) and has a
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Answers

Answer:

y=-2/5x

Step-by-step explanation:

y-y1=m(x-x1)

y-(-2)=-2/5(x-5)

y+2=-2/5(x-5)

y=-2/5x+10/5-2

y=-2/5x+2-2

y=-2/5x

Which speeds are equal to 1/2 mile per hour? Mark all that apply.
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1/10 hour / 1/5 mile
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4/5 mile / 4/10 hour
/

Answers

answer :

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Answers

i think the answer is 1/3 from 8x 6 =-46.7 i think

Find the shaded angle

Answers

Answer:

332°

Step-by-step explanation:

Given is an isosceles triangle,

Measures of base angles of an isosceles triangle are equal.

Therefore,

Measure of central angle

= 180° - ( 76° + 76°)

= 180° - 152°

= 28°

Measure of shaded angle

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Drag each label to the correct location on the tree diagram. Each label can be used more than once, but not all labels will be used.
Brandon is making party decorations by selecting one of two kinds of balloons—heart-shaped balloons or oval-shaped balloons. He puts them in one of three baskets—red, pink, or white. The sample space for the event of selecting a balloon and putting it in one of the baskets is represented in the tree diagram. Complete the sample space.
oval
red
white
pink

Answers

Answer:

He is 100% right

Step-by-step explanation:

Julio's family traveled 3 8 of the distance to his aunt's house on Saturday. They traveled 3 5 of the remaining distance on Sunday. What fraction of the total distance to his aunt's house was traveled on Sunday?

Answers

Answer: [tex]\dfrac{3}{8}[/tex]

Step-by-step explanation:

Given

Julio traveled [tex]\frac{3}{8}[/tex] of distance to his aunt's house on Saturday

they have traveled [tex]\frac{3}{5}[/tex] of the remaining distance on Sunday

suppose the total distance is [tex]x[/tex]

Distance traveled on Saturday

[tex]\dfrac{3x}{8}[/tex]

Remaining distance is

[tex]x-\dfrac{3x}{8}=\dfrac{5x}{8}[/tex]

Distance traveled on Sunday

[tex]\Rightarrow \dfrac{3}{5}\times \dfrac{5x}{8}=\dfrac{3x}{8}[/tex]

The fraction of distance traveled on Sunday is

[tex]\Rightarrow \dfrac{\frac{3x}{8}}{x}=\dfrac{3}{8}[/tex]

A triangle has an area of 230.86 square inches. The height of the triangle is 23.8 inches. What is the length of the base of the triangle?

I'll give brainlist!! Pls help

Answers

Answer:

Length of the base of the triangle = 19.37 inch (Approx.)

Step-by-step explanation:

Given:

Area of given triangle = 230.56 square inches

Height of the triangle = 23.8 inches

Find:

Length of the base of the triangle

Computation:

Area of triangle = (1/2)(b)(h)

Area of given triangle = (1/2)(Length of the base of the triangle)(Height of the triangle)

230.56 = (1/2)(Length of the base of the triangle)(23.8)

461.12 = (Length of the base of the triangle)(23.8)

(Length of the base of the triangle)(23.8) = 461.12

Length of the base of the triangle = 19.37 inch (Approx.)

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Answers

Answer:

9/64

Step-by-step explanation:

3 x 3 is 9 and 8 x 8 is 64 and this fraction cannot be simplified

Exact Form:
√6/4

Or

Decimal Form:
0.61237243…

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What is the value of x?

Answers

Answer:

x = 59

Step-by-step explanation:

combine all four angle measure expressions and set equal to 360°, then solve

x + x + 2x + 3 + 2x + 3 = 360

6x + 6 = 360

6x = 354

x = 59

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Answers

X=-10/3 and y is equal to 10
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Answers

Answer:

10 X 10 X 10

Step-by-step explanation:

if thts what you talking aboyt

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Answers

Step-by-step explanation:

C and D are the correct objectives

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Answers

Step-by-step explanation:

(−3)(+8)

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Answers

There is no horizontal asymptote for this problem .


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Answers

Answer:

C..... I think it is a answer


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Answers

Answer:

Step-by-step explanation:

C and E look good Dani

USING YOUR MATH
5. A circular swimming pool has a diameter of 22 feet. A cover that just fits over the top of the
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(1) 69 sq.ft
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Answers

Answer:

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How would you begin to plot the ordered pair ( 6,2)?

Answers

To graph a point you have a coordinate plane or graph not theirs a x axis with is a like going left to right and a y axis, a line starting up to down. I remember using the saying “run before you jump” meaning you run first starting at your origin(0,0). In this case your first number is 6 for which you would run until you’re at 6 on the x axis line or the line going left to right then jump to straight up because it’s a positive number. Because you’re jumping up you’re going to jump 2 on the y axis line or the line going up and down. Your point doesn’t need to be exactly on either line. Remember your first coordinate or number is the number you run with and the second the one you jump with

The store has 6 blue notebooks, 11 red notebooks, 7 purple notebooks, 5 black notebooks, and 3 green notebooks. What is the probability that Melissa will buy a purple notebook?
7/25
7/32
3/16
11/32

Answers

Answer: 7/32

Step-by-step explanation:

Answer:

7/32

Step-by-step explanation:

i did the test and got it right

Nathan started out on a road trip with his friend Ryan. Nathan picked Ryan up at his house and they started out. Nathan kept track of the distance he was from his house, d, after h hours of driving in the chart below.

Hours

2

4

6

10

Distance

114

224

334

554



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Answers

Answer:

57 mph

Step-by-step explanation:

Half of 114=57.

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Answers

Answer:

8

Step-by-step explanation:

you would add 1+3+4

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Answers

Complete question is;

Scores on a test are normally distributed with a mean of 200 and a standard deviation of 12. Find the probability that a randomly selected student scored less than 218.

Answer:

0.93

Step-by-step explanation:

We are given;

Mean; μ = 200

Standard deviation; σ = 12

Random value; x¯ = 218

Z-score formula is;

z = (x¯ - μ)/σ

z = (218 - 200)/12

z = 18/12

z = 1.5

From z-table, attached, probability = 0.93

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Answers

Answer:

56.5 in

Step-by-step explanation:

Answer:

56.5 in³

Step-by-step explanation:

I wrote out the work in the file below:

A farmer plants the same amount every day, adding up to 134 acres at the end of the year. If the year is 12 over, how many acres has the farmer planted?

Answers

fAnswer:

1608 acres

Step-by-step explanation:

total acres planted in 12 years = acres planted per year x number of years

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Answer:

5/6

Step-by-step explanation:

1 2/3 x 1/2 = 5/6

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Answers

(2,3)
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an expression that is equivalent to 60x+28y.

Answers

Answer:

Step-by-step explanation:

The trick here is to identify the greatest common factor of 60 and 28.  4 is such a factor.  We can therefore rewrite 60x + 28y as

4(15x + 7)

There are other possible answers.

600x + 280y

------------------- is an example.

       100

Simplify: (16-5)-9 x 1 A. 5 B. 2 C. 4 D. 3

Answers

Answer:

B it right...

Step-by-step explanation:

Answer: B 2

Step-by-step explanation:

16 - 5 = 11

11 - 9.1  = 2 option B

In a quiz contest, Mary answers 90% of the questions correctly without any additional clues from the quiz coordinator. The randomly generated numbers below simulate this situation.

The numbers 0 to 8 represent questions answered correctly without additional clues, and the number 9 represents questions that needed additional clues.

44 51 99 66 23
68 72 20 20 59
50 89 39 36 20
90 13 51 47 92
49 20 89 10 13
52 82 52 52 99
28 10 33 35 73
40 44 30 95 22
99 10 55 10 35
36 78 92 37 96
The estimated probability that it would take at least three questions for Mary to need additional clues is (_____)

The estimated probability that Mary needed additional clues to answer two consecutive questions is (_____)

Answers

To solve this problem, we should note that there are:

total questions = 100

questions answered correctly = 90

questions that needed additional clues = 10

1. The first question is to find the probability that in the third question, Mary would need additional clue. Therefore this implies that in the first and second questions, Mary would answer it correctly. Therefore:

Probability = (question 1 answered correctly) * (question 2 answered correctly) * (question 3 needed clue)

Probability = (90/100)*(89/99)*(10/98)

Probability = 0.08256 = 8.26%

2. The second question finds for the probability that two consecutive needs additional clue, therefore:

Probability = (question 1 needed clue) * (question 2 needed clue)

Probability = (10/100)*(9/99)

Probability = 9.1*10^-3 = 0.91%

Answer:

1. The estimated probability that it would take at least three questions for Mary to need additional clues is 0.24

2. The estimated probability that Mary needed additional clues to answer two consecutive questions is 0.06

Step-by-step explanation:

I just took the test! I hope this helps you! <3

from the Deck of 52 cards is drawn at a random . what is the probability of a face card or ace ?​

Answers

Step-by-step explanation:

Given that,

Total no. of cards = 52 (Total no. of outcomes)

There are 12 face cards. No of favorable outcomes = 12

P(E) = favorable outcome/total no of outcomes

So,

[tex]P(F)=\dfrac{12}{52}\\\\=\dfrac{3}{13}[/tex]

There is 4 ace in a deck of 52 cards.

[tex]P(A)=\dfrac{4}{52}\\\\=\dfrac{1}{13}[/tex]

Hence, this is the required solution.

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