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Kay [80]
2 years ago
13

In a lab experiment, the decay of a radioactive isotope is being observed. At the beginning of the first day of the experiment t

he mass of the substance was 500 grams and mass was decreasing by 8% per day. Determine the mass of the radioactive sample at the beginning of the 13th day of the experiment. Round to the nearest tenth (if necessary).
Mathematics
1 answer:
GaryK [48]2 years ago
5 0

Using an exponential function, it is found that the mass of the radioactive sample at the beginning of the 13th day of the experiment was of 169.1 mg.

<h3>What is an exponential function?</h3>

A decaying exponential function is modeled by:

A(t) = A(0)(1 - r)^t

In which:

  • A(0) is the initial value.
  • r is the decay rate, as a decimal.

At the beginning of the first day of the experiment the mass of the substance was 500 grams and mass was decreasing by 8% per day, hence A(0) = 500, r = 0.08, and the equation is given by:

A(t) = A(0)(1 - r)^t

A(t) = 500(1 - 0.08)^t

A(t) = 500(0.92)^t

At the 13th day, the mass is given by:

A(13) = 500(0.92)^{13} = 169.1

More can be learned about exponential functions at brainly.com/question/25537936

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Which relationships describe angles 1 and 2?
coldgirl [10]
Supplementary angles because because angle 1 + angle 2 = 180° so they form a line
6 0
2 years ago
A hot air balloon is descending at a rate of 287 feet per minute.
faust18 [17]

Answer:

Please check the explanation.

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

  • m is the rate of change or slope
  • b is the y-intercept

A hot air balloon is descending at a rate of 287 feet per minute.

Thus, the rate of change m = -287

The negative sign indicates that a hot air balloon is descending.

Let y be elevation.

Let x be the time (in minutes)

As there is no mentioning of the initial height.

Thus, the y-intercept b = 0

now substituting m = -287 and b = 0

y = mx + b

y = -287x + 0

y = -287x

In order to determine the total change in elevation of the balloon in 4 minutes, we need to substitute x = 4 in the equation y = -287x.

Thus, the total change in elevation of the balloon in 4 minutes will be:

y = -287x

y = -287(4)

y = -1148 feet

The negative sign indicates that that the elevation is decreasing.

8 0
3 years ago
Kaylee opened an account with a deposit of $800. The bank pays 4% annual simple interest on this account. Kaylee makes no additi
Snowcat [4.5K]

Answer: the amount of interest that she would earn is $192.

Step-by-step explanation:

We would apply the formula for determining simple interest which is expressed as

I = PRT/100

Where

I represents interest paid on the amount of money deposited.

P represents the principal or amount of money deposited.

R represents interest rate on the deposit.

T represents the duration of the deposit in years.

From the information given,

P = $800

R = 4%

T = 6 years

Therefore,

I = (800 × 4 × 6)/100

I = $192

6 0
3 years ago
19. The numerator of a fraction is 1 less than the denominator.
yulyashka [42]

Let the original fraction be

\dfrac{n-1}{n}

Now let's increase both numerator and denominator by 2:

\dfrac{n+1}{n+2}

This produces a 1/12 increase:

\dfrac{n+1}{n+2}-\dfrac{n-1}{n}=\dfrac{1}{12}

The left hand side can be rearranged as

\dfrac{2}{n^2+2n}=\dfrac{1}{12}

Invert both sides:

\dfrac{n^2+2n}{2}=12 \iff n^2+2n=24

Solve the quadratic equation:

n^2+2n-24=0 \iff n=-6 \lor n=4

So, in the first case, the original fraction is

\dfrac{n-1}{n}=\dfrac{-6-1}{-6}=\dfrac{7}{6}

In the second case, we have

\dfrac{n-1}{n}=\dfrac{4-1}{4}=\dfrac{3}{4}

5 0
3 years ago
One of the roots of the equation x^2-13x+q=0 is 12. Find the other root in the value of the coefficient Q.
fenix001 [56]

Considering that 12 is a root of the function, the value of coefficient Q is of 12.

<h3>What does it means that x is a root of a function f(x)?</h3>


It means that f(x) = 0.

In this problem, the function is given by:

f(x) = x² - 13x + q.

Since 12 is a root, we have that f(12) = 0, hence:

12² - 13 x 12 + q = 0

q - 12 = 0.

q = 12.

More can be learned about functions at brainly.com/question/25537936

#SPJ1

5 0
1 year ago
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