Adrian is going to invest $9,900 and leave it in an account for 10 years. Assuming the interest is compounded continuously, what interest rate, to the nearest hundredth of a percent, would be required in order for Adrian to end up with $17,700?

Part 1) Finding the inverse

Let x = r and y = H(r)

We have the equation y = 6240(1 + x/100)^t which is the same as saying y = 6240(1 + 0.01x)^t since 1/100 = 0.01

From here, swap x and y to get the equation x = 6240(1+0.01y)^t

Let's solve for y

x = 6240(1+0.01y)^t

6240(1+0.01y)^t = x

(1+0.01y)^t = x/6240

1+0.01y = (x/6240)^(1/t)

0.01y = (x/6240)^(1/t)-1

100*0.01y = 100*((x/6240)^(1/t)-1)

y = 100*((x/6240)^(1/t)-1)

y = 100*(x/6240)^(1/t) - 100

This becomes r = 100*(H/6240)^(1/t) - 100 after we replace y with r and x with H. Note the r and H swapped places, just like x and y did. Earlier we had H isolated on the left, but now r is isolated on the left.

We could write r(H) = 100*(H/6240)^(1/t) - 100 to mean the same thing.

So what exactly does this inverse function do? Well the original function tells us the number of households for any given growth rate, which is r.

The inverse function swaps things around to allow us to find the growth rate if we know how many households there are. We're working backwards. In both cases, t is held to some constant fixed value.

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Part 2) Finding the growth rate if the number of households is 7800 after 3 years.

We're going to plug in H = 7800 and t = 3 into the inverse function we found to determine the value of r, or r(H)

r(H) = 100*(H/6240)^(1/t) - 100

r(7800) = 100*(7800/6240)^(1/3) - 100

r(7800) = 7.72173450159419

You'll need your calculator to get this approximate value. After rounding to two decimal places, we get r(7800) = 7.72

Since r = 7.72, this means the growth rate is 7.72%

Answer:

[tex] {25in}^{2} [/tex]

Step-by-step explanation:

see attached image

Answer:

The time it will take is 8hours 45mins.

Step-by-step explanation:

Since y = –240x represents a submarine descent. We are looking for how long, that is the time, it will take for the submarine to make a descent of 2100. We know that y is the elevation, if it is descending it will be in the negative direction, making it -ve.

A descent of 2100 means y = –2100. Hence,

–2100 = –240x

x = –2100/–240 = 8.75hours = 8hours 45minutes. (0.75hours = 3/4hours = 3/4 x 60mins = 45mins).

Answer:

11

Step-by-step explanation:

Creo nose XD (revisa los múltiplos de 11 siempre son pares) xd

Answer:

x = -56/5, -11 1/5, or -11.2

Step-by-step explanation:

5/7x - 14 = -22

5x -98 = -154

5x = -154 + 98

5x = -56

x = -56/5, -11 1/5, or -11.2

Answer:

x= -11.2

Step-by-step explanation:

5/7x-14=-22

      +14 +14        Add 14 on both sides

  5/7x = -8        

(7/5)*5/7x = -8*(7/5)     Multiply by the reciprocal on both sides to leave x alone

  x= -11.2      Answer

Answer:

60

Step-by-step explanation:

2a is more than 90 so it is more likely to be 120

so divide that by 2 and 60

Answer:i think a=120

Answer:

The answer is 18

Step-by-step explanation:

18 + x really means 18 + 0, because x is equal to 0

and if 18 + x = y, it means 18 + 0 = y,

so y is equal to 18

hope this helped!

Answer:

115 m

Step-by-step explanation:

4 + 9 + 6 + 4 = 23 cm

23 x 5 = 115 m

Answer:

4/30 or 4/120

Step-by-step explanation:

Answer:

volume = Pi(2x^2+3x-5) x (2x+5)^2    or     P1(8x^4+52x^3+100x^2-125)

Step-by-step explanation:

radius = (4x+10)/2 = 2x+5

volume = Pi(2x^2+3x-5) x (2x+5)^2

volume = Pi(2x^2+3x-5) x (4x^2+20x+25)

volume = P1(8x^4+52x^3+100x^2-125)

Answer:

[tex]y-(9)=(-8)(x-8)\\[/tex]

Step-by-step explanation:

[tex](x_1, y_1) = (8, 9)\\(x_2, y_2) = (9,1)\\[/tex]

Step one: Find the slope (m)

[tex]slope=m=\frac{rise}{run} =\frac{y_2-y_1}{x_2-x_1} = \frac{1-9}{9-8} =\frac{-8}{1} =-8[/tex]

Step two: Plug your known values into the point-slope equation

[tex]m=-8\\y_1=9\\x_1=8\\[/tex]

Point-slope form is [tex]y-y_1=m(x-x_1)[/tex]

[tex]y-(9)=(-8)(x-8)\\[/tex]

If you want to convert point-slope form to general form, isolate for y.

[tex]y-9=-8x+64\\y=-8x+73[/tex]

mag Aral ka wag ka mag hanap Ng sagot

Answer:

y= 5/7x -2.7

Step-by-step explanation:

Y= mx + c                             (-3,-3)   (4,2)

                                           x1  , y1     x2, y2

to find m (gradient)

y^2 - y^1 / x^2 - x^1

2-(-3) / 4 - (-3)

5/7                               m = 5/7

take (4,2)  and gradient and substitute

2=5/7(4) + c

2=4.7+ c

2-4.7 = c

-2.7 = c

now we have c and m so just put it in the equation

y= 5/7x -2.7

Answer:

i think it is b but i am not 100%

sorry if i am wrong

Step-by-step explanation:

Answer:

11a - 8b.

Step-by-step explanation:

7a + 4(a-2b)

= 7a + 4a - 8b

= 11a - 8b.

Answer:

infinitely many solutions cuz in mathmatices any problem has solution

Answer:

y=5/3x+-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

raduis and diameter.

Hi there,

Answer is: 4 months, because 4 plus 4 is 8.

Explanation: 4/1/2 ; 8/1/2

How to get 4/1/2 ; 8/1/2

So you add 4 to get 8 and 4 plus 4 is 8.

Answer:

<Ber=<kem(vertically opposite angle)

9x-17=3x+31

9x-3x=31+17

6x=48

x=48/6=8

<kem=3×8+31=55°is answer

Answer:

x = 9/11

Step-by-step explanation:

5x = -6x + 9

Add 6x to both sides

11x = 9

Divide both sides by 11

x = 9/11

Answer:
X Equals 9/11

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable. So X will equal 9/11, which in decimal form is 0.81.

The alternate interior angles shown are <3 and <5, as well as <2 and <8.

I hope this helped!

Answer:

ur answer would be

<2 and <5

step-by-step explanation:

hope this helps

Answer: 4f^2 -4f+1

Step-by-step explanation:

2f-1)^2

This is equal to

(2f-1) * (2f-1)

FOIL

first: 2f*2f = 4f^2

outer: 2f*-1 = -2f

inner: -1*2f = -2f

Last = -1*-1 = 1

Add them together: = 4f^2 -2f-2f+1

Combine like terms 4f^2 -4f+1

Answer:

(2f-1)(2f-1)

2f^2-2f-2f+1

2f^2-4f+1

Answer:

Game =$6 and ride=$9, to solve is 3x+4y=54

x+y=15

Step-by-step explanation:

;)

Answer:

h = [tex]\frac{3v}{\pi r^{2} }[/tex]

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

0.25

Step-by-step explanation:

Reciprocal of a number is 1÷ that number

1÷4= 0.25

awnscer is 6.72 sorry could not find a diagram

Answer:

The answer is 6.72

Step-by-step explanation:

what you can do is 42 x 16 (you can add the decimal if you want) btu after your done solving it you should get 672 and if your doing decimals just count how many behind the decimal and count it and you will get 6.72! hope this helps.