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
vladimir1956 [14]
3 years ago
6

Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 3%. If the rate of deca

y is proportional to the amount of the substance present at time t, determine the half-life of the radioactive substance. (Round your answer to one decimal place.)
Mathematics
1 answer:
Hitman42 [59]3 years ago
6 0

Answer:

The half-life of the radioactive substance is 135.9 hours.

Step-by-step explanation:

The rate of decay is proportional to the amount of the substance present at time t

This means that the amount of the substance can be modeled by the following differential equation:

\frac{dQ}{dt} = -rt

Which has the following solution:

Q(t) = Q(0)e^{-rt}

In which Q(t) is the amount after t hours, Q(0) is the initial amount and r is the decay rate.

After 6 hours the mass had decreased by 3%.

This means that Q(6) = (1-0.03)Q(0) = 0.97Q(0). We use this to find r.

Q(t) = Q(0)e^{-rt}

0.97Q(0) = Q(0)e^{-6r}

e^{-6r} = 0.97

\ln{e^{-6r}} = \ln{0.97}

-6r = \ln{0.97}

r = -\frac{\ln{0.97}}{6}

r = 0.0051

So

Q(t) = Q(0)e^{-0.0051t}

Determine the half-life of the radioactive substance.

This is t for which Q(t) = 0.5Q(0). So

Q(t) = Q(0)e^{-0.0051t}

0.5Q(0) = Q(0)e^{-0.0051t}

e^{-0.0051t} = 0.5

\ln{e^{-0.0051t}} = \ln{0.5}

-0.0051t = \ln{0.5}

t = -\frac{\ln{0.5}}{0.0051}

t = 135.9

The half-life of the radioactive substance is 135.9 hours.

You might be interested in
Determining Sine and Cosine Values
marysya [2.9K]

Is there an attachment?

6 0
3 years ago
Find the value of the length <br> x<br> rounded to 1 DP.
bagirrra123 [75]

Length of x is 98.2 m

<u>Step-by-step explanation:</u>

Step 1:

Use the trigonometric ratio tan 27° to find the common side of both the right angled triangles.

tan 27° = opposite side/adjacent side = opposite side/9

∴ Opposite side = 9 tan 27° = 9 × - 3.27 = -29.46 m

Step 2:

Use this side and trigonometric ratio cosine to find the value of x.

cos 49° = adjacent side/x = -29.46/x

∴ x = -29.46/cos 49° = -29.46/0.30

     = 98.2 m (negative value neglected)

5 0
3 years ago
Read 2 more answers
Function Composition:<br> Let the function <img src="https://tex.z-dn.net/?f=f%28x%29%3D%203%2B6x" id="TexFormula1" title="f(x)=
V125BC [204]

Answer:

<u>Given </u>

  • f(x) = 3 + 6x

A

<u>Find the inverse of f(x):</u>

  • x = 3 + 6f⁻¹(x)
  • 6f⁻¹(x) = x - 3
  • f⁻¹(x) = (x - 3) / 6

B

  • f · f⁻¹( ∛5/6) =
  • f( f⁻¹( ∛5/6)) =
  • f((∛5/6 - 3)/6) =
  • 3 + 6((∛5/6 - 3)/6) =
  • 3 + ∛5/6 - 3 =
  • ∛5/6

C

  • f · f⁻¹(x) =
  • f(f⁻¹(x)) =
  • f((x - 3)/6) =
  • 3 + 6(x - 3)/6 =
  • 3 + x - 3 =
  • x
4 0
3 years ago
The cost to a rent paddle boat at the county park is $8 per hour if x represent the number off hours the boat is rented and for
bazaltina [42]

Answer:

10+8x=y

Step-by-step explanation:

The 10$ is added on because it's a one time exchange and the 8 is multiplied by the x because for every hour you add 8$ to the price and y is the total price at the end depending on x.

4 0
2 years ago
Which of the following operations could you perform on both sides of the given equation to solve it? check all that apply. 8x -
antiseptic1488 [7]
8x-2x=24+6
6x=30
6x/6=30/6
x=5
3 0
3 years ago
Other questions:
  • Elise wrote all possible four-digit numbers using two of the digit 2 and two of the digit 0. Two of Elise’s numbers have a great
    14·1 answer
  • O(●︿●)o ! <br> -1/3 x (-3/7)
    9·2 answers
  • Consider the expression –3(y – 5)2 – 9 + 7y.
    13·2 answers
  • 2. The Walton College of Business was ranked 24th out of all public business schools in the United States in 2005. The dean attr
    5·1 answer
  • A birds wingspan is the distance from the tip of one wing to the tip of the other a California condor can have the wingspan of 9
    9·1 answer
  • Which of the following is equal to the fraction below ? (5/9) ^ 8 A. A. 8(5/9) (5 ^ 8)/(9 ^ 8) B. (5 ^ 8)/9 5/(9 ^ 8)
    8·1 answer
  • What is 1/2, 3/4, and 5/48 ordered least to greatest
    5·2 answers
  • Be sure yo write 3-4 sentences.
    11·1 answer
  • Which expression is equivalent to 45.1+3.3?
    13·1 answer
  • CAN SOMEONE HELP ME OUT I BEG U
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!