Are the following functions exponential growth or decay?
Graphing Exponentials

a) f(x)=10(2)x

is this exponential growth? or exponential decay?

b) f(x)=2(0.5)x

is this a exponential growth? or exponential decay?

Answer:

A function is increasing when the gradient is positive

A function is decreasing when the gradient is negative

Question 7

If you draw a tangent to the curve in the interval x < -2 then the tangent will have a positive gradient, and so the function is increasing in this interval.

If you draw a tangent to the curve in the interval x > -2 then the tangent will have a negative gradient, and so the function is decreasing in this interval.

If you draw a tangent to the curve at the vertex of the parabola, it will be a horizontal line, and so the gradient at x = -2 will be zero.

The function is increasing when x < -2

[tex](- \infty,-2)[/tex]

The function is decreasing when x > -2

[tex](-2, \infty)[/tex]

Additional information

We can actually determine the intervals where the function is increasing and decreasing by differentiating the function.

The equation of this graph is:

[tex]f(x)=-2x^2-8x-8[/tex]

[tex]\implies f'(x)=-4x-8[/tex]

The function is increasing when [tex]f'(x) > 0[/tex]

[tex]\implies -4x-8 > 0[/tex]

[tex]\implies -4x > 8[/tex]

[tex]\implies x < -2[/tex]

The function is decreasing when [tex]f'(x) < 0[/tex]

[tex]\implies -4x-8 < 0[/tex]

[tex]\implies -4x < 8[/tex]

[tex]\implies x > -2[/tex]

This concurs with the observations made from the graph.

Question 8

This is a straight line graph. The gradient is negative, so:

The function is decreasing for all real values of x

[tex](- \infty,+ \infty)[/tex]

But if they want the interval for the grid only, it would be -4 ≤ x ≤ 1

[tex][-4,1][/tex]

Question 9

If you draw a tangent to the curve in the interval x < -1 then the tangent will have a negative gradient, and so the function is decreasing in this interval.

If you draw a tangent to the curve in the interval x > -1 then the tangent will have a positive gradient, and so the function is increasing in this interval.

If you draw a tangent to the curve at the vertex of the parabola, it will be a horizontal line, and so the gradient at x = -1 will be zero.

The function is decreasing when x < -1

[tex](- \infty,-1)[/tex]

The function is increasing when x > -1

[tex](-1, \infty)[/tex]

The total number of grams of the supplement in one capsule will be 0.45 grams.

The measurement of any quanity is expressed by its unit. Now the units for the same matter can be expressed in different ways for higher quanity or lower quanity so we need to convert the units for the calculations.

Here in the question

Each capsule has 450 miligrams of supplement.

Total grams in one capsule will be calculated by unit conversion

[tex]\rm 1 \ gram=1000\ miligram\\\\\\1 \ Mg=\dfrac{1}{1000}\ gram\\\\\\450\ Mg=\dfrac{450}{1000}\ gram\\\\\\450 Mg=0.45\ gram[/tex]

Hence the total number of grams of the supplement in one capsule will be 0.45 grams.

To know more about Unit conversion follow

https://brainly.com/question/21196956

#SPJ1

Answer:

       [tex]\huge\boxed{\sf 10x^2-13x-3}[/tex]

Step-by-step explanation:

[tex]=(2x-3)(5x+1)\\\\=2x(5x+1)-3(5x+1)\\\\Distribute\\\\= 10x^2+2x-15x-3\\\\= 10x^2-13x-3\\\\\rule[225]{225}{2}[/tex]

[tex]\text{ The discriminant is 0 if the quadratic expression is a perfect square.}\\\\~~~~~b^2 -4ac =0\\\\\implies k^2-4\cdot 1 \cdot 36 = 0\\ \\\implies k^2 - 144 = 0\\\\\implies k^2 = 144\\\\\implies k = \pm\sqrt{144}\\\\\implies k= \pm12\\\\\text{Hence}~ k=12 ~\text{and}~ k=-12.[/tex]

Let's solve this problem step-by-step

Let's set:

   2x + 6y = 36 -- equation 1

   x + 4y = 20 -- equation 2

(equation 2) * 2

   2x + 8y = 40 -- equation 3

(equation 3) - (equation 1)

   2y = 4

   y = 2 -- equation 4

Plug (equation 4)'s value of y into (equation 2)

   x + 4(2) = 20

   x = 20 - 8

   x = 12

Thus x = 12 and y = 2

Let's check, by substituting these values

  [tex]2x + 6y = 36\\2(12)+6(2) = 36\\24+12=36\\36=36\\\\x+4y=20\\12+4(2)=20\\12+8=20\\20=20[/tex]

Answer: x = 12 and y = 2

Hope that helps!

Answer:

30 Pages

Step-by-step explanation:

Make a ratio:

[tex]\frac{3}{6} =\frac{x}{60}[/tex]

Cross multiply:

180=6x

Divide both sides by 6:

x=30

Answer:

30

Step-by-step explanation:

divide 60 by 6 and you get 10. Then take 10 and times it by 3

The equation is  4^{3x} is equal to 8^{1/x} 2^{x+3} and the values of x are x is equal to (3+√69)/(10) or x is equal to (3-√69)/(10)

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]

where 'a' is a constant and a>1

After following the rules to model the equation.

The equation becomes:

[tex]\rm 4^3^x= 8^{1/x}\times 2^{x+3}[/tex]

After solving, we get:

[tex]2^{6x}= 2^{3/x \ +x+3}[/tex]  (power rule)

Taking log on both sides with base 2

[tex]\rm log_2(2^{6x})= log_2(2^{3/x \ +x+3})[/tex]

After solving, we will get a quadratic equation:

[tex]\rm 5x^2-3x-3 = 0[/tex]

After using quadratic formula, we will get,

[tex]\rm x=\dfrac{3+\sqrt{69}}{10}[/tex] or

[tex]\rm x=\dfrac{3-\sqrt{69}}{10}[/tex]

Thus, the equation is  4^{3x} is equal to 8^{1/x} 2^{x+3} and the values of x are x is equal to (3+√69)/(10) or x is equal to (3-√69)/(10)

Learn more about the exponential function here:

brainly.com/question/11487261

#SPJ1

Answer:

Step-by-step explanation:

Selling price = Cost price + Marked price - discount

            s   =  c + m - d

Answer:

Step-by-step explanation:

A. 403.43

I hope it's help

Answer:

it's C

Step-by-step explanation:

i took the test and got it right

Answer:

it's [C]  I got it right on my test

Step-by-step explanation:

Answer:

212

Step-by-step explanation:

starting with (xy)

you first plug in x=2 and y=3

(2×3) = 6

then we add in the exponent of 3

6^3 = 216

this is because an exponent shows you how many times the number is multiple by itself (6×6×6)

next we work on x^4 by plugging in x=2

2^4=16

2×2×2×2

we do the same for x^2

2^2=4

2×2

next we do the division

16/4=4

finally we take the 216 and 4 and do the subtraction

216-4=212

The equation of the value of the car over a year is 2357.14x + y = 33,000. Then the value of the car 4 years after it was purchased is $23571.43.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

A new car is purchased for $33,000 and overtime its value depreciates by one half every 7 years.

Then the value of the car is given by the linear equation. Then the line is passing through (0, $33,000) and (7, $16,500). Then we have

Let y be the value of the car and x be the number of years. Then we have

[tex]\rm y \ - \ 33000 \ \ = -\dfrac{16,500}{7} (x-0)\\\\y+2357.14x = 33000[/tex]

Then the value of the car 4 years after it was purchased, to the nearest hundred dollars will be

[tex]\begin{aligned} \rm y +2,357.14 \times 4 &= 33,000\\\\\rm y + 9,428.57 &= 33,000\\\\\rm y &= 23,571.43 \end{aligned}[/tex]

More about the linear system link is given below.

https://brainly.com/question/20379472

#SPJ1

Answer:

csc C  = 5/3 = 1. (6)

Step-by-step explanation:

Given:

∠B = 90° is a right angle

AB = 30

We know that:

sec A = 5/3 = 1/ cos A = 1/ ( adjacent side/hypothenuse) =

hypothenuse/ adjacent side to angle A

csc C = 1/ sin C = 1/ sinC = 1/ (opposite side /hypothenuse) =

hypothenuse/ opposite side to angle C

Note that :

adjacent side to angle A is the same as opposite side to angle C

Therefore sec A = csc C  = 5/3 ( fraction form) = 1.(6) (decimal form)

Answer: D.

Step-by-step explanation:

The equation [tex]f(x) = (x-1)^{2} - 2[/tex] works only for option D. If x is 2, for example, the equation would look like this: [tex]f(2) = (2-1)^{2} - 2[/tex]. This equals [tex](1)^{2} - 2[/tex] which equals negative one. Therefore, when x is 2, y is -1. All of the graphs have the point (2, -1). We can still tell though that it is not A or B because there are spaces in between the points. If x = 2.2, the equation would not work for A or B because there is not a point with an x value of 2.2. This is different for both C and D. Δ

Answer C ends off early. There are endpoints to the figure. If x = 4, the equation would not work. This is because there is no point in answer C that has an x value of 4. On the other hand, question D does have a point with an x value of 4.

If x = 4, the equation looks like [tex]f(4) = (4-1)^{2} - 2[/tex].

We can simplify this to [tex]f(4) = (3)^{2} - 2[/tex]

and then [tex]f(4) = 7[/tex]

This means that when x is 4, y is 7. This is true for no graph but option D. Therefore the answer to this problem is D.

Answer:

6 art course and 7 writing coures

Answer:

907.9 in²

Step-by-step explanation:

D = 2r

r = D/2

r = 34/2

r = 17 in

A = πr²

A = π(17)²

A = 289π

A ≈ 907.9 in²

The equation of the directrix to the right of the center is equal to 2.8.

Given the following data:

(x - 1)²/9 - (y - 2)²/16 = 1.

Mathematically, the standard equation of the directrix lines for a hyperbola of the form (x - h)²/a² - (y - k)²/b² = 1 is given by:

x = h ± a²/√(a² + b²)

Where:

Substituting the given parameters into the standard equation, we have;

x = 1 ± a²/√(a² + b²)

x = 1 ± 9/√(9 + 16)

x = 1 ± 9/√25

x = 1 ± 9/5

x = 1 + 9/5

x = 1 + 1.8

x = 2.8.

Read more on directrix here: https://brainly.com/question/2346582

Answer: The answer is 2.8

Step-by-step explanation:

Answer:

The median of the lower half of the data was determined to be 67 while the median of the upper half of the data was determined to be 92.

Step-by-step explanation:

Step 1:  Order from least to greatest

51, 56, 62, 72, 79, 81, 82, 85, 89, 95, 97, 98

Step 2:  Determine the median of the lower half of the data

There are 12 numbers which means that there is going to be 6 numbers on both sides of the data.  So using the first 6 numbers we will be able to determine the median of the lower half of the data.

51, 56, 62, 72, 79, 81

Since there is an even amount of numbers, that means that we will need to find the middle between the 3rd and 4th number.  We can do that by adding them up together and dividing by 2.

(62 + 72) / 2 = 67

Step 3:  Determine the median of the upper half of the data

So using the first 6 numbers we will be able to determine the median of the upper half of the data.

82, 85, 89, 95, 97, 98

Since there is an even amount of numbers, that means that we will need to find the middle between the 3rd and 4th number.  We can do that by adding them up together and dividing by 2.

(89 + 95) / 2 = 92

Answer: The median of the lower half of the data was determined to be 67 while the median of the upper half of the data was determined to be 92.

solving the equation given to us first:

-5x/2 = 5/1 ( ignore the ≤ symbol for now and replace with =) and cross multiply

you will get

-5x = 10

x = -10/5 ( minus doesn't stay in denominator so so we take up to numerator )

x = -2

so x ≤ -2

NOTE: if we have ≤ we shade the dot but if we have just < or we don't shade the dot.

soooo

x ≤ -2 will be going backwards

so the answer is option (C).

Hope this helps.

Good luck.

Answer:5

Step-by-step explanation: Divide 60 By 12

Answer:

the answer is 5 rocks.

Step-by-step explanation:

Sinice there are 12 boxes and has 60 rocks. So that means we will divide the two to get 5bwhich is in each box.

The number of students in the survey said that math was their favorite subject is given by: Option D: 123

Conditional relative frequency is relative frequency conditional to some special characteristic.

For this case, we're specified the following table:

[tex]\begin{array}{cccc}&\text{Math}&\text{Other favorite subject}&\rm Total\\\text{Male}&0.35&0.65&1.0\\\text{Female}&0.45&0.55&1.0\\\rm Total &0.41&0.59&1.0 \end{array}[/tex]

It is given that:

We have to find how many students in the survey said that math was their favorite subject.

From males, 0.35 out of 1 male said math was their favorite subject. (since total in male is 1, showing that the row of males got conditional relative frequency conditional to the gender male, and relative to the total count of males).

Thus, as out of 1, there was 0.35 supporter of math (from males), so from 120 male students, there were [tex]120\times 0.35 = 42[/tex] male students who had chosen math as their favorite subject.

Similarly, 0.45 per 1 female student chose their favorite subject as math.

Since there are 180 female students, therefore, total [tex]180\times 0.45 = 81[/tex] female students had chosen math as their favorite subject.

So, total 42+81=123 students had chosen math as their favorite subject.

Thus, the number of students in the survey said that math was their favorite subject is given by: Option D: 123

Learn more about conditional relative frequency here:

https://brainly.com/question/12165221

Answer: D-123

Step-by-step explanation:

Answer:

6*5=30

Step-by-step explanation:

Answer: 30

Step-by-step explanation: it means multiply 6 by 5

Answer:

47

Step-by-step explanation:

2820 = 2 * 2 * 3 * 5 * 47

Prime factors:

2, 3, 5, 47

Largest prime factor:

47

Step-by-step explanation:

The largest prime factors of 2820 is 2*2*3*5*47 is the answer

Answer:

•The function models exponential decay

•The rate of decay is 75%

•350 represents the amount of money Alicia had in the budget at the beginning of the summer

•Alicia spent $262.50 during the first week of summer

Based on the calculations, the number of Jamal's triangle that are obtuse are: C. 3.

In order to determine an obtuse triangle, we would apply Pythagorean theorem:

c² = a² + b²

Where:

For an obtuse triangle, the square of the hypotenuse is greater than the sum of the square of both the adjacent and opposite side:

c² > a² + b²

For Triangle 1, we have:

7² > 6² + 3²

49 > 36 + 9

49 > 45 (obtuse triangle).

For Triangle 2, we have:

8² > 6² + 3²

64 > 36 + 9

64 > 45 (obtuse triangle).

For Triangle 3, we have:

8² > 7² + 3²

64 > 49 + 9

64 > 58 (obtuse triangle).

For Triangle 4, we have:

8² > 6² + 7²

64 > 36 + 49

64 < 85 (not obtuse triangle).

Read more on Pythagorean theorem here: https://brainly.com/question/16176867

#SPJ1

Answer: the answer is C 3.

Step-by-step explanation: it show below.

Answer: x = 2

Step-by-step explanation:

Answer:

2nd one - blue triangle

Step-by-step explanation:

A right angle triangle is a triangle that has a angle of 90°

Therefore our answer is second one - blue triangle.

Hope this helps and branliest please

Answer:

2nd triangle.

Step-by-step explanation:

For a triangle to be considered as a eight triangle it should have one angle which is equal to 90° in measure.

Here, the second triangle has 90° & hence is a right triangle.

________

Hope it helps ⚜

Answer:

option B

option C

4:40pm

2:45pm

option d

3:30

Step-by-step explanation:

please consider as brainlest que.

Answer:

0.667x

Step-by-step explanation:

150% = x

100% = ?

=> 100% * x / 150% = 0.667x