what is the percent rate of change in function y = (0.98) ^ x? determine whether the function represents exponential growth or exponential decay​

Answers

Answer 1

C. 2%; exponential decay

Answer 2

You can use the fact that increasing power of values lying between 0 and 1 results in less and less values.

The percent rate of change in given function is -2%

The function represents exponential decay.

Given that:The function: [tex] y = (0.98) ^ x[/tex]To find:Percent rate of change in given function.Is it representing exponential growth or exponential decay?

Finding percent rate of change in given function:


For finding this, first find how much the output y changes if we change x from x to x + 1.

Output when x = x:   [tex]y = (0.98)^x[/tex]

Output when x = x+1:  [tex]y = (0.98)^{x+1}[/tex]

Difference in output if x goes from x to x+1: [tex](0.98)^{x+1} - (0.98)^x = (0.98)^x(0.98 - 1) = -0.02 \times (0.98)^x[/tex] (this change occurs if we increase input x by 1 unit, thus this also represents the rate)

Rate of change of function per unit increment = [tex]-0.02 \times (0.98)^x[/tex]

The percentage of rate of change is found as:

[tex]\text{Percent rate of change\:} = \dfrac{\text{Rate of change} \times 100}{\text{previous value}} = \dfrac{-0.02 \times (0.98)^x \times 100}{(0.98)^x} \\\\ \text{Percent rate of change\:} = -2\%[/tex]

Thus, the percent rate of change is -2%

The negative sign shows that the value is decreasing, thus showing that function shows exponential decay.

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Related Questions

Could somebody please help me with these?? It's due tomarrow

Answers

Example for Table 1:

y = x + 6

So if X=-8

1st Row -8+6=-2

2nd Row -4+6=2

3rd Row -2+ 6=4

4th Row -9+6=-3

5th Row 2+6=8

So for any table, the X in the table rule is the X that you are working on.

Answer:

i got you:

1) -2, 2, 4, -3, 8

2) 37, -3, 29, -67, -75

3) -36, 4, -4, -20, -12

4) -10, 6, -4, 8, 4

5) -2, 18, -16, 6, -10

6) -4, -15, 2, 0, -6

7) -25, 23, 5, 29, 11

8) 24, 38, -60, 3, 10

9) 2, 4, 9, -1, -3

10) -14, -8, -15, -10, -16

11) 9, 18, -21, -3, -24

12) -10, 35, -73, 71, -19

hope that helps

Step-by-step explanation:

Below are two parallel lines with a third line intersecting them.

Answers

Answer:

77

Step-by-step explanation:

180-103=77

What is the solution for -3w-4=w+4

Answers

Answer:

uhh

Step-by-step explanation:

carrot?

the answer is to this question is w=-2

Classify this triangle by its sides?

Answers

Answer:

Scalene

Step-by-step explanation:

First option, scalene

i need to drag one into the box to match them

Answers

Answer:

54÷9 = 6 so for the second box is 6 hot dogs per person

54÷27= 2 third box is 2 hot dogs per person

54÷54= 1 fourth box is 1 hot dog per person

What is m∠DEF?
Enter your answer in the box.

There is a triangle DEF in which side DE is congruent to side EF and G is the midpoint of the side DF. Segment EG intersect the side DF at point G. The measure of angle DEG is (3y+4) degrees and the measure of angle FEG is (5y-10) degrees.

Answers

Answer:

m<DEF = 8y - 6

Step-by-step explanation:

Given that: DEG = [tex](3y +4)^{o}[/tex], and FEG = [tex](5y-10)^{o}[/tex].

The given triangle is an isosceles triangle with sides DE ≅ DF.

But,

m<DEF = DEG + FEG

            =  [tex](3y +4)^{o}[/tex] + [tex](5y-10)^{o}[/tex]

            = 3y + 4 + 5y - 10

            = 8y - 6

m<DEF = 8y - 6

Therefore, the measure of < DEF is 8y - 6.

I will give you 15 points

Answers

Answer: A, D

Step-by-step explanation:

Simplify: (3x-4)+(-2x+8).

Answers

Answer:

Step-by-step explanation:

x+4

- IZ
- -
M = 9
7. Carlene has $300 in her wallet but she doesn't realize that she has a hole in her wallet!
Every step she takes, she loses five dollars. How far will she walk before she only has $150 left
in her wallet? Write a sentence explaining your solution.
Click to add text
Explanation:
ick to add speaker notes

Answers

Step-by-step explanation:

Subtract initial amount (300) and final (150). from there you get 150 dollars that was lost. We know that every step you 5 dollars so then divide 150 and 5 to get 30. So the distance was 30 steps.

Over the summer Marty reads 4 times as many pages as the number of pages Nelson and Jennifer read combined Marty reads 1,860 pages and Nelson reads 240 pages

Answers

She reads 4 timws as many pages as them together so you add the number of pages they eead them mhltiply it by 4 (1860+240)4=8400

what are the relative max and min. of this graph?

Answers

Relative Max is 6

Relative Min is -8

Please help, I will be giving brainlist.

Answers

Answer:

b

Step-by-step explanation:

Answer:

o B 6 inches.

Step-by-step explanation:

Proportions:

13 in ⇔  9.75 in

8 in  ⇔   X  in

X = 8*9.75/13

X = 6 in

Here are the ingredients to make 12 cupcakes.
For 12 cupcakes
200 g butter
200 g caster sugar
4 eggs
250 g flour
Mark is making cupcakes to sell at his school play.
Mark wants to make 1 cupcake for each adult and 2 cupcakes for each child.
There will be 152 adults and 80 children at the school play.
Mark can get these ingredients from the school kitchen.
5 kg butter
5 kg caster sugar
90 eggs
5 kg flour
Make a shopping list of any ingredients Mark still needs, showing the amount of each
ingredient.

Answers

Answer:

Mark needs 2 kg butter, 2 kg caster sugar, 14 eggs, and 1.5 kg flour.

Step-by-step explanation:

Alright, first you double the number of kids, as Mark wants each kid to have two cupcakes, not one. (Then add 80+80 to get 160)

Now add the adults to children: 160+152=312

now divide by 12 to see how many batches of cupcakes he needs to make.

312÷12=26 So he needs to make 26 batches

Now here are the ingredients needed to make 12 batches of cupcakes (I multiplied the amount of each ingredient by 26)

5200 g (5.2 kg) butter, 5200 g (5.2 kg) caster sugar, 104 eggs, and 6500 g (6.5 kg) flour.

now make the measurements the same as Mark's ingredients (or the other way around)

(to save time I am not showing each one, just the normal ingredients turned into kg and compared)

5 kg butter < 5.2 kg butter

5 kg caster sugar < 5.2 kg butter

90 eggs < 104 eggs

5 kg flour < 6.5 kg flour

Now do a little subtraction.....

5.2 kg-5 kg = 2 kg butter is needed....

5.2 kg - 5 kg = 2 kg caster sugar is needed....

104 - 90 = 14 eggs needed....

6.5 kg - 5 kg = 1.5 kg flour needed....

And there you go!!! Hope this helped!!! :D

The amount of ingredients that Mark still requires after getting it from the kitchen is needed.

The amount of ingredients Mark still needs is

200 g of butter

200 g of caster sugar

14 eggs

1500 g of flour

The number of cupcakes that are needed for 152 adults and 80 children is

[tex]152+2\times 80=312[/tex]

For the 12 cupcakes the ingredients are

200 g butter

200 g caster sugar

4 eggs

250 g flour

For 1 cupcake the ingredients are

[tex]\dfrac{200}{12}=\dfrac{50}{3}\ \text{g}[/tex] of butter

[tex]\dfrac{200}{12}=\dfrac{50}{3}\ \text{g}[/tex] of caster sugar

[tex]\dfrac{4}{12}=\dfrac{1}{3}[/tex] eggs

[tex]\dfrac{250}{12}=\dfrac{125}{6}\ \text{g}[/tex] of flour

For 312 cupcakes

[tex]312\times \dfrac{50}{3}=5200\ \text{g}[/tex] of butter

[tex]312\times \dfrac{50}{3}=5200\ \text{g}[/tex] of caster sugar

[tex]312\times \dfrac{1}{3}=104[/tex] eggs

[tex]312\times \dfrac{125}{6}=6500\ \text{g}[/tex] of flour

The required ingredients are

[tex]5200-5000=200\ \text{g}[/tex] of butter

[tex]5200-5000=200\ \text{g}[/tex] of caster sugar

[tex]104-90=14[/tex] eggs

[tex]6500-5000=1500\ \text{g}[/tex] of flour

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3. Ivan has completed 45% of his walk.
He has already walked 9 km. How much farther does he have left to walk?​

Answers

Answer:

11

Step-by-step explanation:

The required distance left to the walk will be 11 km.

What is the percentage?

The percentage is defined as a ratio expressed as a fraction of 100.

Let the total distance of the walk would be x km

As per the given information, the required solution would be as:

⇒ 45% of x = 9

45%  is expressed as 45/100 in fractional form

⇒ (45/100)x = 9

45/100  is expressed as 0.45 in decimal form

⇒ 0.45x = 9

⇒ x = 9/0.45

⇒ x = 20

So the total distance of the walk is 20 km

Since he has already walked 9 km.

So, he has left to the distance of the walk = 20 - 9 = 11 km

Therefore, the required distance left to the walk will be 11 km.

Learn more about the percentages here:

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John and Robin like to collect stones. John has n stones, and Robin has 68 stones. Together they have a total of 98 stones, Write an equation to describe this situation. ​

Answers

Answer:

n+68=98 find n (n=30)

Step-by-step explanation:

13 Points. Find the perimeter.

Answers

Answer:

15.7 cm

Step-by-step explanation:

The perimeter of the entire circumference is

entire perimeter = 2п r

п = 3.14 (aprox)

r = radius = 3cm

entire perimeter = 2*3.14*3 = 18.84 cm

the entire perimeter of the circumference corresponds to 360 degrees

then,

proportions:

18.84 cm ⇔ 360°

F cm ⇔  300°

F = 18.84*300/360

F = 15.7 cm

You pay $11.20 to buy drink boxes for the football team. Each drink box cost $0.40. How many drink boxes did
you buy?

Answers

I think it’s uhhhh I think it’s uhhhhh carrot

Help me out please and thank you ;)

Answers

Answer : d
Explanation:
Shoe size and letters in your name have nothing to do with each other
Done it before, the answer is D

Brian can iron 3 shirts in 5 minutes. If Brian irons at a constant rate, how many shirts can he iron in 30 minutes? WILL GIVE BRANLIEST

Answers

Answer:

18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

30/5 = 6

6 * 3 = 18

4.3 m to centimeters

Answers

Answer: 430 cm

Step-by-step explanation:

Answer:

430 cm

Step-by-step explanation:

43 multiplied by 10 is 430

Solve 6 - 5x = 7 + 3x

Answers

Answer:

hol up

x=-1/8  negative one over eight

Step-by-step explanation:

convert 2 3/4 into a improper faction ​

Answers

Answer:

11/4

Step-by-step explanation:

2 times 4 equals 8 and plus 3 equals 11 and dem is 4 so 11/4

Answer:

[tex]\frac{11}{4}[/tex]

Step-by-step explanation:

[tex]2\frac{3}{4}[/tex]

To get an improper fraction do the multiply and add shortcut.  Do the denominator times the whole number ( 2 x 4).  You will get 8, next add 8 with 3.  You still keep the denominator, so your final result is [tex]\frac{11}{4}[/tex]

what is 65% of 80 ??????????????

Answers

Answer:

Step-by-step explanation:

65% of 80 is

65*80/100=52

Answer:

52

Step-by-step explanation:

Calculate percentage:

'Percentage' is obtained by multiplying 80 by 65%.

65% × 80 =

(65 ÷ 100) × 80 =

(65 × 80) ÷ 100 =

5,200 ÷ 100 =

52

Checking:

How do we check the result?

If 65% × 80 = 52 =>

Divide 52 by 80...

... And see if we get as a result: 65%.

Calculate the percent value:

52 ÷ 80 =

0.65 =

0.65 × 100/100 =

(0.65 × 100)/100 =

65/100 =

65%

A new watch costs $120 at the store. If it goes on sale for 75% off and has a sales tax of 6%, what is the final cost of the watch?

Answers

The final cost is $ 100

Can you guys please help me!!

Answers

32 it’s as simple as 4(5) + 12

Answer:

a. 32

b. 32

Step-by-step explanation:

a. 12 + 4y

They gave us the value of "y" which is "5", and substitute that into the expression.

12 + 4y

12 + 4(5)

12 + 20

32

b. 4 (y + 3)

They gave us the value of "y" which is "5", and substitute that into the expression.

4 ( y + 3 )

4 ( 5 + 3)

Distributive property (multiply what is in the parenthesis by what is out of it (4))

4 * 5 + 4 * 3

20 + 12

32

Hope this helped!

Have a supercalifragilisticexpialidocious day!

What are the answers to these questions

Answers

F(-1)=2
F(2)=-1
F(3)=-3



The f(x) part is the input and the stuff after is the output

The slope of the line below is 5. Which of the following is the point-slope form
of the line?
(-1,3)
5
A. y + 3 = -5(x - 1)
B. y + 3 = 5(x - 1)
C. y - 3 = 5(x+1)
D. Y-3 = -5(x + 1)

Answers

The point-slope form of the line in the graph is y-3 = 5(x+1). The correct option is C.

What is the point-slope form of the line?

The point-slope form of the line is y-y₁ = m( x-x₁)

Here, m is the slope of the line.

The graph given in the question has a slope of 5

It passes through the point ( -1,3)

The point slope form of the line is

y - 3 = 5 ( x - (-1))

y-3 = 5(x+1)

This is represented by option C.

To know more about the Point-slope form of the line

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Which expression is equivalent to?

Answers

I think it is the third one from the top

1 and 2 is all I need and you guys would help me from not getting beat

Answers

Answer:

1. -10

2. -11

Step-by-step explanation:

Rewrite in y=mx+b form
- (y + 2) = 2(2x + 1)

Answers

Answer:

y=-4x-4

Step-by-step explanation:

Answer:

y=-4x+4

Step-by-step explanation:

Use order of operations, PEMDAS, to put it in y=mx+b form.

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