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aliya0001 [1]
3 years ago
9

Use the exponential decay​ model, Upper A equals Upper A 0 e Superscript kt​, to solve the following. The​ half-life of a certai

n substance is 19 years. How long will it take for a sample of this substance to decay to 78​% of its original​ amount? It will take approximately nothing years for the sample of the substance to decay to 78​% of its original amount.
Mathematics
1 answer:
Akimi4 [234]3 years ago
5 0

Answer:

It will take 7 years ( approx )

Step-by-step explanation:

Given equation that shows the amount of the substance after t years,

A=A_0 e^{kt}

Where,

A_0 = Initial amount of the substance,

If the half life of the substance is 19 years,

Then if t = 19, amount of the substance = \frac{A_0}{2},

i.e.

\frac{A_0}{2}=A_0 e^{19k}

\frac{1}{2} = e^{19k}

0.5 = e^{19k}

Taking ln both sides,

\ln(0.5) = \ln(e^{19k})

\ln(0.5) = 19k

\implies k = \frac{\ln(0.5)}{19}\approx -0.03648

Now, if the substance to decay to 78​% of its original​ amount,

Then A=78\% \text{ of }A_0 =\frac{78A_0}{100}=0.78 A_0

0.78 A_0=A_0 e^{-0.03648t}

0.78 = e^{-0.03648t}

Again taking ln both sides,

\ln(0.78) = -0.03648t

-0.24846=-0.03648t

\implies t = \frac{0.24846}{0.03648}=6.81085\approx 7

Hence, approximately the substance would be 78% of its initial value after 7 years.

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Find the value of f(x) at the given value of x: f(x) = (x -4)(x + 3), x = 3​
mario62 [17]

Answer:

-6

Step-by-step explanation:

f(x)= (3- 4)(3+3)

=( -1 )(6)

= -6

7 0
2 years ago
PLZ HELP ASAP One pump fills a tank 4 times as fast as another pump. If the pumps work​ together, they fill the tank in 20 minut
svp [43]
It takes the faster pump 12 minutes to fill the tank.

Since the faster truck can produce 60% more than the other truck. 60% of 20 minutes is 12.
3 0
3 years ago
(2b) A rectangular prism measures 2 & 2/5 inches by 3 & 1/5 inches by 2 inches. How many cubes with edge length 1/5 inch
erastova [34]

Answer:

1920 cubes.

Step-by-step explanation

Turn both the mix numbers into improper fractions.

2 2/5 = 12/5

3 1/5 = 16/5

Then you will turn 1/5 into its reciprocal and multiply both the improper fractions by it. You can just casually multiply 2 and 5.

12/5 * 5/1 = 12

16/5 * 5/1 = 16

2 * 5 = 10

Next you multiply all together to get 1920 cubes.

(I could be missing a step. I apologize if I did.)

3 0
3 years ago
10
MissTica

The graph of the inequality will be B. on a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.

<h3>How to get the graph?</h3>

It can be deduced that the coordinates satisfy the equation of the line.

3y = 2x - 12

Divide through by 3.

y = 2/3x - 4.

The slope is 2/3.

In conclusion, the correct option is B.

Learn more about inequalities on:

brainly.com/question/14074138

#SPJ1

5 0
2 years ago
Powers of 5
Korvikt [17]

Answer:

divide the previous value by 5

Step-by-step explanation:

125/5 = 25

25/5 = 5

5/5 = 1

1/5 = ⅕

7 0
3 years ago
Read 2 more answers
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