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omeli [17]
3 years ago
11

Determining Exponential Growth and Decay in Exercise, use the given information to write an exponential equation for y. Does the

function represent exponential growth or exponential decay?
dy/dt = 2y, y = 10 when t = 0
Mathematics
1 answer:
Cerrena [4.2K]3 years ago
4 0

Answer:

y=10e^{2t}

Growth function

Step-by-step explanation:

We are given that

\frac{dy}{dt}=2y

y=10 when t=0

Taking integration on both sides then we get

\int \frac{dy}{y}=\int 2dt

lny=2dt+C

Using formula

\int\frac{dx}{x}=lnx,\int dx=x

y=e^{2t+C}

y=e^C\cdot e^{2t}=Ce^{2t}

ln x=y\implies x=e^y

e^C=Constant=C

Substitute y=10 and t=0

10=C

Substitute the value of C

y=10e^{2t}

When t tends to infinity then

\lim_{t\rightarrow \infty}=\lim_{t\rightarrow\infty}10e^{2t}=\infty

Hence, the exponential function is growth function.

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Answer:

x = - 30

Step-by-step explanation:

x/3  + 8 = - 2     subtract 8 from both sides of the equation

x/3 = -2 - 8 = -10  now multiply both sides by 3

x = -30

3 0
2 years ago
Cual es la raiz cuadrada de 202
bezimeni [28]

Answer:

14.2126704036

Step-by-step explanation:

8 0
3 years ago
Find the smallest value of k such that the LCM of<br> k and 6 is 60
Advocard [28]

Answer: The smallest valuest value for<em> k </em>is 10, such that LCM o<em>f k</em> and 6 is 60.

Step-by-step explanation:

We know that, LCM = Least common multiple.

For example : LACM of 12 and 60  is 60.

If LCM of k and 6 is 60.

i.e. the least common multiple of k and 6 is 60.

Since, 10 x 6 = 60.

The smallest valuest value for<em> k </em>should be 10, such that LCM o<em>f k</em> and 6 is 60.

Hence, the smallest value of k is 10.

5 0
3 years ago
If f(3)=5 and f(4)=8 what does f(5)= and f(6)=
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4 0
3 years ago
A rectangles width is 4 less than its area and its length is 19. what is it’s width?
Alchen [17]

The width of the rectangle is \frac{2}{9} unit

Step-by-step explanation:

The given is:

  • A rectangles width is 4 less than its area
  • Its length is 19 units

We need to find the width of the rectangle

Assume that the width of the rectangle is x units

∵ The area of the rectangle = length × width

∵ The width of the rectangle = x units

∵ The length of the rectangle = 19 units

∴ The area of the square = 19 × x = 19 x units²

∵ The width of the rectangle is 4 less than its area

- That means subtract 4 from the area to find the width

∴ x = 19 x - 4

- Subtract 19 x from both sides

∴ -18 x = -4

- Divide both sides by -18

∴ x = \frac{-4}{-18}

- Reduce the fraction by dividing up and down by -2

∴ x = \frac{2}{9}

The width of the rectangle is \frac{2}{9} unit

Learn more:

You can learn more about the rectangles in brainly.com/question/12919591

#LearnwithBrainly

4 0
3 years ago
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