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
Anastasy [175]
3 years ago
9

A storage tank contains a liquid radioactive element with a half-life of 96 years. It will be relatively safe for the contents t

o leak from the tank when 0.02% of the
radioactive element remains. How long must the tank remain intact for this storage procedure to be safe?
The tank must remain intact for years.
(Round the base of the exponential function to four decimal places. Then round the final answer to the nearest year as needed.)

Mathematics
1 answer:
PolarNik [594]3 years ago
5 0

Answer:

The tank must remain intact for 1183 years.

Step-by-step explanation:

Exponential equation for decay:

The amount of a substance after t years is given by:

A(t) = A(0)e^{rt}

In which A(0) is the initial amount and r is the decay rate.

A storage tank contains a liquid radioactive element with a half-life of 96 years.

This means that A(96) = 0.5A(0), and we use this to find r.

A(t) = A(0)e^{rt}

0.5A(0) = A(0)e^{96r}

e^{96r} = 0.5

\ln{e^{96r}} = \ln{0.5}

96r = \ln{0.5}

r = \frac{\ln{0.5}}{96}

r = -0.0072

So

A(t) = A(0)e^{-0.0072t}

It will be relatively safe for the contents to leak from the tank when 0.02% of the radioactive element remains. How long must the tank remain intact for this storage procedure to be safe?

This is t for which A(t) = 0.0002A(0). So

A(t) = A(0)e^{-0.0072t}

0.0002A(0) = A(0)e^{-0.0072t}

e^{-0.0072t} = 0.0002

\ln{e^{-0.0072t}} = \ln{0.0002}

-0.0072t = \ln{0.0002}

t = -\frac{\ln{0.0002}}{0.0072}

t = 1183

The tank must remain intact for 1183 years.

You might be interested in
Identify the diameter using the following radius: 16 ft.
Firlakuza [10]
B this answer is 4 it’s correct
7 0
3 years ago
In an August 2012 Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 536 said that they were dissatisfied w
soldier1979 [14.2K]

Answer:

Yes, result is significant ; PVALUE < α

Step-by-step explanation:

Given :

x = 536

n = sample size = 1012

Phat = x / n = 536 / 1012 = 0.5296 = 0.53

H0 : P0 = 0.5

H1 : P0 > 0.5

Test statistic :

(Phat - P0) ÷ sqrt[(P0(1 - P0)) / n]

1-P0 = 1 - 0.5 = 0.5

(0.53 - 0.5) ÷ sqrt[(0.5*0.5)/1012]

0.03 ÷ 0.0157173

= 1.9087

Pvalue :

Using the Pvalue from test statistic :

Pvalue = 0.02815

To test if result is significant :

α = 0.05

0.02815 < 0.05

Pvalue < α ; Hence, result is significant at α=0.05; Hence, we reject H0.

3 0
3 years ago
'Five times a number minus eight is 17.5.
11Alexandr11 [23.1K]

Answer:

5.1

Step-by-step explanation:

you need to work backwards.

so do 17.5 + 8 then divide by 5 to get 5.1

i hope this helps :)

8 0
2 years ago
Help me please!! The next model of a sports car will cost 12.2% less than the current model. The current model costs $34,000. Ho
andrey2020 [161]

Answer:

the price will decrease by 4148

the price of the next model will be 29852

7 0
2 years ago
How to find horizontal and vertical asymptotes from equations?
julsineya [31]
This is how u would find horizontal and vertical asymptotes

6 0
3 years ago
Other questions:
  • Which of the following is the conjugate of a complex number with 2 as the real part and −8i as the imaginary part?
    12·2 answers
  • If a/b=p/q, then a + b/b = p + b/q.<br> True<br> False
    12·1 answer
  • Please help me with this. Not very good with scatter plots.
    12·1 answer
  • What is the value of x? Enter your answer in the box.
    8·1 answer
  • Kyle is purchasing a refurbished phone. He is looking at the phone models 4, 5, and 6, with a protective case in red (R), blue (
    6·2 answers
  • A model car is 6.9 centimeters long and 3.5 centimeters wide. find the real length of the car. Round your answer to the nearest
    11·1 answer
  • what is a linear function and a nonlinear fuction and how can you tell if the ordered pairs go to them
    11·1 answer
  • The Celsius temperature, C, of a chemical reaction increases and then decreases over time according to the
    9·1 answer
  • Susan makes 5 fruit cups for the picnic. In each cup, she has 5 strawberries and 3 kiwi. Joanna uses the same number of total fr
    6·2 answers
  • Which of the following are examples of professional organizations in the field of IT
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!