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1 year ago

What is the rate of decay in the following function? f(x)=3(67)^x

Mathematics

1 answer:

tigry1 [53]1 year ago

5 0

Answer:

Suppose N is the size of a population of radioactive atoms at a given time t, and dN is the amount by which the population decreases in time dt; then the rate of change is given by the equation dN/dt = −λN, where λ is the decay constant.

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Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning.

natka813 [3]

Suppose that the height (in centimeters) of a candle is a linear function of

the amount of time (in hours) it has been burning.

Let x be the amount of time in hours

Let y be the heoght of a candle in centimeters

The two points are then as (9,24.5) and (23,17.5).

$\mathrm{Find\:the\:line\:}\mathbf{y=mx+b}\mathrm{\:passing\:through\:}\left(9,\:24.5\right)\mathrm{,\:}\left(23,\:17.5\right)$

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(9,\:24.5\right),\:\left(x_2,\:y_2\right)=\left(23,\:17.5\right)$

$m=\frac{17.5-24.5}{23-9}$

$m=-0.5$

$\mathrm{Plug\:the\:slope\:}-0.5\mathrm{\:into\:}y=mx+b$

$y=\left(-0.5\right)x+b$

$\mathrm{Plug\:in\:}\left(9,\:24.5\right)\mathrm{:\:}\quad \:x=9,\:y=24.5$

$24.5=\left(-0.5\right)\cdot \:9+b$

$-4.5+b=24.5$

$b=29$

$\mathrm{Construct\:the\:line\:equation\:}\mathbf{y=mx+b}\mathrm{\:where\:}\mathbf{m}=-0.5\mathrm{\:and\:}\mathbf{b}=29$

$y=-0.5x+29$

Now plug in x=21, we get

$y=-0.5*21+29=18.5$

Thus the height of the candle after 21 hours is 18.5 centimeters.

7 0

3 years ago

MATH HELP???

marin [14]

<h2>Answer:</h2>

The quadratic function are:

option: A A) y(y + 4) - y = 6

Option: C C.) 4b(b) = 0

<h2>Step-by-step explanation:</h2>

We know that the general equation of a quadratic equation in terms of a variable x is given by:

$ax^2+bx+c=0$

y(y + 4) - y = 6

On simplifying the terms we have:

$y^2+4y-y=6\\\\y^2+3y-6=0$

Hence, option: A is correct.

(3x + 2) + (6x - 1) = 0

$(3x + 2) + (6x - 1) = 0\\\\i.e.\\\\3x+2+6x-1=0\\\\i.e.\\\\3x+6x+2-1=0\\\\i.e.\\\\9x+1=0$

Hence, it is a linear equation.

Hence, option: B is incorrect.

4b(b) = 0

it could also be written as:

$4b^2=0$

Hence, it is a quadratic equation.

Hence, option: C is correct.

3a - 7 = 2(7a - 3)

$3a-7 = 2(7a-3)\\\\i.e.\\\\3a-7=14a-6\\\\\\i.e.\\\\14a-6-3a+7=0\\\\i.e.\\\\14a-3a-6+7=0\\\\i.e.\\\\11a+1=0$

which is again a linear equation.

Hence, option: D is incorrect.

6 0

3 years ago

Twenty-four students took a test. Fourteen students earned an A and 10 students earned a B. A student will be randomly chosen.

Alex_Xolod [135]

The probability of a student that earned an A on the test is 7/12.

To get a fraction like this, you put the number of students on the left, or the top and the number of students total on the right, or bottom. Then, you simplify your answer. This brings us to 7/12. You cannot simplify any further because the fraction includes a prime number.

I hope this helps!

6 0

2 years ago

Read 2 more answers

What is the best unit to describe the rate at which water flows through a household faucet

andrew11 [14]

The answer should be gallons per minute

5 0

3 years ago

2. The table below shows that the distance d varies directly as the time t. Find the constant of variation and the equation whic

Artemon [7]

<h2><u>Problem Solving</u>:-</h2>

2. The table below shows that the distance d varies directly as the time t. Find the constant of variation and the equation which describes the relation.

<h2><u>Solution</u>:-</h2>

Since the distance d varies directly as the time t, then d = kt.

Using one of the pairs of values, (2, 20), from the table, substitute the values of d and t in d = kt and solve for k.

$\sf{\rightarrow{d = kt}}$