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2 years ago

Does each equation represent exponential decay or exponential growth?

Mathematics

1 answer:

Elden [556K]2 years ago

8 0

Answer:

decay: a, b

growth: c, d, e, f

neither: g

Step-by-step explanation:

A function is exponential if it has the independent variable in an exponent. g(x) is a linear function, not an exponential function.

An exponential function is a growth function if the coefficient of the variable is positive and the base of the exponent is greater than 1. It is a decay function if the exponent is positive and the base is less than 1.

The first two functions are decay functions. The remaining four exponential functions are growth functions.

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3(x - 5) – 3 = 5(x - 2) + 2x

Arlecino [84]

Answer:

x=−2

Step-by-step explanation: Step 1: Simplify both sides of the equation.

3(x−5)−3=5(x−2)+2x

(3)(x)+(3)(−5)+−3=(5)(x)+(5)(−2)+2x(Distribute)

3x+−15+−3=5x+−10+2x

(3x)+(−15+−3)=(5x+2x)+(−10)(Combine Like Terms)

3x+−18=7x+−10

3x−18=7x−10

Step 2: Subtract 7x from both sides.

3x−18−7x=7x−10−7x

−4x−18=−10

Step 3: Add 18 to both sides.

−4x−18+18=−10+18

−4x=8

Step 4: Divide both sides by -4.

−4x

−4

x=−2

6 0

3 years ago

Mrs. Baker conducted a survey in her classroom to determine what the students preferred to do during the summer break. Her surve

navik [9.2K]

Answer:

B. 840

Step-by-step explanation:

21 is 70% of 30 and 70% of 1,200 is 840.

4 0

3 years ago

Read 2 more answers

NEED HELP FAST<br> 30nPOINTS FOR BRAINLIEST<br><br><br> √5x + √6 = √9

vodka [1.7K]

$\sqrt{5x}$ + √6 = √9

The first step is to get $\sqrt{5x}$ by itself. We can do this by subtracting $\sqrt{6}$ from each side, and simplifying $\sqrt{9}$

$\sqrt{5x}$ = 3 - $\sqrt{6}$

Now we square both sides

5x = (3 - $\sqrt{6}$ )²

Using the formula (a - b)² = a² -2ab + b², (3 - $\sqrt{6}$ )² = 15 - 6 $\sqrt{6}$

5x = 15 - 6 $\sqrt{6}$

x = $\frac{15 - 6\sqrt{6}}{5}$

8 0

3 years ago

Read 2 more answers

A perpendicular bisector, , is drawn through point C on .

Liula [17]

Answer:

The x-intercept of CD is B(18/5,0). The point C(32,-71) lies on the line CD.

Step-by-step explanation:

the x-intercept of CD is[ A(3,0) B(18/5,0) C(9,0) D(45/2,0) ] . Point [ A(-52,117) B(-20,57) C(32,-71) D(-54,-128) ] lies on CD.

Given :

CD is perpendicular bisector of AB.

The coordinates of point A are (-3, 2) and the coordinates of point B are (7, 6).

C is the midpoint of AB.

$C=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{7-3}{2},\frac{2+6}{2})=(2,4)$

The coordinates of C are (2,4).

Line AB has a slope of: $m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{6-2}{7-(-3)}=\frac{4}{10}=\frac{2}{5}$

The product of slopes of two perpendicular lines is -1. Since the line CD is perpendicular to AB, therefore the slope of CD : $m_2=-\frac{5}{2}$

The point slope form of a line is given by:

$y-y_1=m(x-x_1)$

The slope of line CD is $-\frac{5}{2}$ and the line passing through the point (2,4), the equation of line CD can be written as:

$y-4=-\frac{5}{2}(x-2)\\y=-\frac{5}{2}x+5+4\\y=-\frac{5}{2}x+9 .... (1)$

The equation of CD is $y=-\frac{5}{2}x+9$

In order to find the x-intercept, put y=0.

$0=-\frac{5}{2}x+9\\\frac{5}{2}x=9\\x=\frac{18}{5}$

Therefore the x-intercept of CD is B(18/5,0).

Put x=-52 in eq(1).

$y=-\frac{5}{2}(-52)+9=139$

Put x=-20 in eq(1).

$y=-\frac{5}{2}(-20)+9=59$

Put x=32 in eq(1)

$y=-\frac{5}{2}(32)+9=-71$

Put x=-54 in eq1).

$y=-\frac{5}{2}(-54)+9=144$

Thus, only point (32,-71) satisfies the equation of CD. Therefore the point C(32,-71) lies on the line CD.

8 0

3 years ago

In 2003, the population of an African country was about 22.5 million people, which is 2 million more than 5 times the population

Anton [14]

Answer:

Population in 1950 was 4,100,000

Step-by-step explanation:

Equation: 5x + 2,000,000 = 22,500,000

Subtract 2,000,000 from each side: 5x = 20,500,000

Divide each side by 5: x = 4,100,000

I hope this helps, please mark Brainliest, thank you!

3 0

3 years ago