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Montano1993 [528]
1 year ago
13

Identify whether the equation represents an exponential growth or exponential decay function.1. y = 1/4 (1/e)^-2x2. y = (1/e)^4x

3. y = 2e^-x + 1How do you do this?
Mathematics
1 answer:
zvonat [6]1 year ago
5 0

The general formula for exponential growth and decays is:

y=y_0e^{kx}

if k>0 then then it is an exponential growth function. If k<0 then the function represents an exponential decay.

Now we need to classify each of the functions:

1.

The function

y=\frac{1}{4}(\frac{1}{e})^{-2x}

can be wrtten as:

\begin{gathered} y=\frac{1}{4}(e^{-1})^{-2x}^{} \\ =\frac{1}{4}e^{2x} \end{gathered}

comparing with the general formula we notice that k=2, therefore this is an exponential growth.

2.

The function

y=(\frac{1}{e})^{4x}

can be written as:

\begin{gathered} y=(\frac{1}{e})^{4x} \\ y=(e^{-1})^{4x} \\ y=e^{-4x} \end{gathered}

comparing with the general formula we notice that k=-4, therefore this is an exponential decay.

3.

The function

y=2e^{-x}+1

comparing with the general formula we notice that k=-1, therefore this is an exponential decay.

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“Write an equation and solve for the unknown” I know it’s a lot but can someone help me with this
Svetradugi [14.3K]

Answer:

g) x = 30

h) x = 30

i) m = 55

j) x = 24

k) k = 45

Step-by-step explanation:

G)

all angles of a triangle add up to 180.

the square in the bottom right of the triangle is 90 btw

2x + x + 90 = 180

3x + 90 = 180

3x + 90 - 90 = 180 - 90

3x = 180 - 90

3x = 90

3x/3 = 90/3

x = 30

H)

this is an Isosceles triangle.

that means the bottom two angles are equal.

75 + 75 + x = 180

x + 150 = 180

x + 150 - 150 = 180 - 150

x = 180 - 150

x = 30

I)

2m is supplementary to the bottom right angle of the triangle.

that means they add together to make 180.

80 + 30 + (180 - 2m) = 180

110 - 2m = 180 - 180

110 - 2m = 0

110 = 2m

110/2 = m

55 = m

J)

to save time I'm not going to write out the steps, its the same as the i.

2x + 3x + (180 - 120 ) = 180

5x + 60 = 180

5x = 180 - 60

5x = 120

x = 120/5

x = 24

K)

imagine this as a triangle and a square.

sorry I'm not sure how to explain this -.-

but the equation would be

k + k + 90 = 180

2k + 90 = 180

2k = 180 - 90

2k = 90

k = 45

L)

Im not sure how to solve this, I'm sorry :( hope you figure it out!

5 0
3 years ago
Endpoint 1: (-1,2)<br> Midpoint: (9,-6)<br> Endpoint 2=
Vlad [161]

Answer:

(19 , -14)

Step-by-step explanation:

Find the distance in between each x & y for a coordinate.

Let: (x₁ , y₁) = (-1 , 2)

Let: (x₂ , y₂) = (9 , -6)

From x₁ ⇒ x₂: 9 - (-1) = 10

From y₁ ⇒ y₂: -6 - 2 = -8 = 8*

*Remember that distance cannot be negative, but for the sake of this question, we will leave it as -8.

The distance between the x points are in intervals of 10. The distance between the y points are in intervals of 8. Add 10 & subtract 8 to their respective numbers to get endpoint 2:

(9 (+ 10) , -6 (- 8)) = (19 , -14)

Endpoint 2 = (19 , -14)

~

7 0
3 years ago
I need help thank you
avanturin [10]

Answer:

The area is 252

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=%7Bx%7D%5E%7B%20log_%7B3%7D%28x%29%20%7D%20%20%3D%2081%20%7Bx%7D%5E%7B3%7D%20" id="TexFormula1
BlackZzzverrR [31]

Answer:

x=81 or 1/3

Step-by-step explanation:

x^\log_3(x)} =81x^3\\\log_3(x^{\log_3(x)})=\log_3(81x^3)\\\(\log_3x)(\log_3x)=\log_381+\log_3x^3\\(\log_3x)^2=3\log_3x^+4\\\\Let u=\log_3x\\\\u^2-3u-4=0\\(u-4)(u+1)=0\\u=4 \\4=\log_3x\\x=3^4=81\\\\u=-1\\-1=\log_3x\\x=3^{-1}=1/3

3 0
3 years ago
Tanner collected 360 cans and bottles while fundraising for his baseball team. This was 40% of what Reggie collected. How many c
Vanyuwa [196]
The amount Reggie collected is equal to x
\frac{360}{.4}= \frac{x}{1}

x =  \frac{360}{.4} =  \frac{360}{ \frac{4}{10} } =  \frac{360*10}{4} = 900


4 0
3 years ago
Read 2 more answers
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