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3 years ago

Given an exponential function for compounding interest, A(x) = P(.91)^x, what is the rate of change?

Mathematics

2 answers:

PilotLPTM [1.2K]3 years ago

8 0

Answer:

Option B = -9%

Step-by-step explanation:

Given : Given an exponential function for compounding interest, $A(x) = P(.91)^x$

To find : What is the rate of change?

Solution :

The general form of the exponential function is $f(x)=a(1+r)^x$

Where,

r is the rate of change

if r> 1 then it is growth rate

if r< 1 then it is decay rate.

Comparing given function with exponential function,

$A(x) = P(.91)^x$

$1+r=0.91$

$r=0.91-1$

$r=−0.09$

It is a decay rate.

Convert into percentage, multiply with 100

$-0.09\times 100=-9\%$

Therefore, Option B is correct.

The rate of change is -9%.

Marina CMI [18]3 years ago

7 0

The confirmed correct answer is -9%. Trust me.

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White raven [17]

The answer is C and your welcome

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3 years ago

Use differentiation rules to find the values of a and b that make the function f(x) = ( x 2 if x ≤ 2, ax3 + bx if x > 2 diffe

Maurinko [17]

Answer:

The values of a and b are $a=\frac{1}{4}$ and b = 1

Step-by-step explanation:

* Lets explain how to solve the equation

f(x) = {x² x ≤ 2

{ax³ + bx x > 2

* We need to find the values of a , b that make the function

differentiable at x = 2

- At first for f(x) to be continuous at x = 2, substitute x by two in the

the two expressions and equate them

∵ f(x) = x² at x ≤ 2 and f(x) = ax³ + bx at x > 2

∴ f(2) = (2)² = 4 ⇒ (1)

∴ f(2) = a(2)³ + b(2)

∴ f(2) = 8a + 2b ⇒ (2)

- Equate (1) and (2)

∴ 8a + 2b = 4 ⇒ (3)

* For f(x) to be differentiable when x = 2, the function must be

continuous when x = 2 and the one-sided derivatives must be

equal when x = 2

# Remember: If $f(x)=ax^{b}$ , then $f'(x)=abx^{b-1}$

If $f(x)=ax$ , then $f'(x)=a$

If $f(x)=a$ , then $f'(x)=0$

∵ f(x) = x²

∴ f'(x) = 2x

- Substitute x by 2

∴ f'(2) = 2(2) = 4

∴ f'(2) = 4 ⇒ (4)

∵ f(x) = ax³ + bx

∴ f'(x) = 3ax² + b

- substitute x by 2

∴ f'(2) = 3a(2)² + b

∴ f'(2) = 12a + b ⇒ (5)

- Equate (4) and (5)

∴ 12a + b = 4 ⇒ (6)

* Now we have system of equations

8a + 2b = 4 ⇒ (3)

12a + b = 4 ⇒ (6)

- Multiply equation (6) by -2 to eliminate b

∴ -24 a - 2b = -8 ⇒ (7)

- Add equations (3) and (7)

∴ -16a = -4

- Divide both sides by -16

∴ a = $\frac{1}{4}$

- substitute the value of a in equation (6)

∴ $12(\frac{1}{4})+b=4$

∴ 3 + b = 4

- Subtract 3 from both sides

∴ b = 1

* The values of a and b are $a=\frac{1}{4}$ and b = 1

5 0

4 years ago

Complete the following statement of congruence: MON~= .

AlexFokin [52]

Answer:

C. RTS

Step-by-step explanation:

When two triangles are congruent, they will have congruent vertices, like each vertex has a partner.

Take a look at the shape of the triangle.

If you look at the triangle on the right, you can see it is almost like a right triangle.

"R" is at the right angle. "S" is on the short side and "T" is on the long side.

In the triangle on the left, "M" is at the right angle. "N" is on the short side and "O" is on the long side.

Thus, the pairs of congruent angles are:

M ≅ R

O ≅ T

N ≅ S

When you write the statement of congruence between triangles, order the letters by their congruent pair.

MON ≅ RTS

8 0

3 years ago

Brainliest goes to whoever answers correctly

velikii [3]

The answer is b

If you plug those values on a graph it will show a straight line.

7 0

3 years ago

Find the value of x and each angle if m angle SOP= (7y-2) and m angle SOR = (5y+14)

Semmy [17]

Answer:

x = 14

m∠SOP = (7x - 2)° = 96°

m∠SOR = (5x + 14) = 84°

Step-by-step explanation:

`From the given picture,

Angle SOP and angle SOR are the linear pairs.

Therefore, sum of these angles will be equal to to 180°.

m∠SOP + m∠SOR = 180° -----(1)

Since, m∠SOP = (7x - 2)° and m∠SOR = (5x + 14)°

[There is a misprint in this question. There should be x in place of y in the measures of the angles]

By substituting these values in the equation (1),

(7x - 2) + (5x + 14) = 180

12x + 12 = 180

12x = 180 - 12

12x = 168

x = $\frac{168}{12}$

x = 14

m∠SOP = (7x - 2)° = 96°

m∠SOR = (5x + 14) = 84°

5 0

3 years ago