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3 years ago

8

Which graph represents exponential decay?

2 answers:

almond37 [142]3 years ago

8 0

I wanna say the first graph because I’m pretty sure the second one shows growth

Reika [66]3 years ago

4 0

Answer: the first graph

Reasoning: When a graph is going left to right it is a decay while when it’s going right to left it is an increase... think of linear equations where if it is going from left to right the slope is negative, it’s the same for the exponential decay and increase.

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Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

5 0

3 years ago

Read 2 more answers

I have many students are represented in the data set?

nalin [4]

Answer:

a) 19 students

b) the mean 3 9/19

the median 3

the mode 3

c) the range 6

Step-by-step explanation:

The data set shows that

0 points gets 1 student,

1 point gets 1 student,

2 points get 2 students,

3 points get 6 students,

4 points get 4 students,

5 points get 3 students and

6 points get 2 students.

a) There are 1+1+2+6+4+3+2=19 students.

b) The mean is

$\dfrac{1\cdot 0+1\cdot 1+2\cdot 2+6\cdot 3+4\cdot 4+3\cdot 5+2\cdot 6}{19}=\dfrac{66}{19}=3\dfrac{9}{19}.$

The average score is 3 9/19 points.

The median is 10th term in the data set - 3 points (means the middle score in the data set)

The mode is 3 points (means most happened score)

c) The range of the data is 6-0=6 points.

7 0

3 years ago

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 4 . If there were

Kamila [148]

If there were 5 yes votes for every 4 no votes, there were 5 yes votes for every 9 total votes, so 5/9 of the 7911 votes were yes. 5/9*7911=4395.

7 0

3 years ago

Plz help plz plz plz plz

inysia [295]

................................................

The answer is 15.

8 0

3 years ago

Read 2 more answers

Given the function f(x) = 6x2 + 3<br> Find f(-2)<br> -22<br> 27<br> 9<br> 15

Andrews [41]

Answer:

27

Step-by-step explanation:

Out of those numbers and assuming the equation is f(x) = 6x^2=3

f(-2)= 6(-2)^2+3

8 0

3 years ago