Kylie invested $290 in an account paying an interest rate of 2.5% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $390?

Answers

Answer 1

Answer:

t= 11.9

Step-by-step explanation:

Compounded Continuously:

A=Pe^{rt}

A=Pe  

rt

 

A=390\hspace{35px}P=290\hspace{35px}r=0.025

A=390P=290r=0.025

Given values

390=

390=

\,\,290e^{0.025t}

290e  

0.025t

 

Plug in

\frac{390}{290}=

290

390

​  

=

\,\,\frac{290e^{0.025t}}{290}

290

290e  

0.025t

 

​  

 

Divide by 290

1.3448276=

1.3448276=

\,\,e^{0.025t}

e  

0.025t

 

\ln\left(1.3448276\right)=

ln(1.3448276)=

\,\,\ln\left(e^{0.025t}\right)

ln(e  

0.025t

)

Take the natural log of both sides

\ln\left(1.3448276\right)=

ln(1.3448276)=

\,\,0.025t

0.025t

ln cancels the e

\frac{\ln\left(1.3448276\right)}{0.025}=

0.025

ln(1.3448276)

​  

=

\,\,\frac{0.025t}{0.025}

0.025

0.025t

​  

 

Divide by 0.025

11.8506326=

11.8506326=

\,\,t

t

t\approx

t≈

\,\,11.9

11.9

Round to the nearest tenth of a year


Related Questions

Nikea went running three days in a row. She ran 3 1/2 miles on Monday. She ran the same distance on Tuesday as she did on Wednesday. She ran a total of 7 1/4 miles on all three days. Which of these equations can be used to find the numbers of miles, x, that Nikea ran on Tuesday and Wednesday? Select all that apply.

A. 2x=7 1/4−3 1/2

B. 2x +3 1/2 = 7 1/4

C. 3 1/2 + x + x = 7 1/4

D. 3 1/2 + x = 7 1/4

E. 7 1/4 + 3 1/2 =2x

Answers

Answer; A B and C are the correct answers also please do not follow the other links answer

Step-by-step explanation:

A restaurant makes cornbread. For each batch of cornbread
3/4
cups of sugar is needed. If the chef used 21 cups of sugar, how
many batches of cornbread did he make?

Answers

Answer:

18

3/4 equals to .75 if you multiply .75 with 21 you get 18

Find the distance to the nearest hundredth between the points A (1,-4) and B
(9,5).

Answers

you can use this formula i couldn’t type it as proper as it’s written so here it is you can easily substitute the x and y :)

If anyone could answer this, i would be most grateful!

Answers

Answer:

C. 10 and 3

Step-by-step explanation:

How to do surface area- cylinder worksheet

Answers

Answer:

to find surface area of cylinder

A=2πrh+2πr²

Step-by-step explanation:

2w+4w+3=8-5w+6

solve pls. no links!!!​

Answers

the answer is w=1 your welcomw

Answer:

w = 1

Step-by-step explanation:

2w + 4w + 3 = 8 - 5w + 6

combine like terms:

6x + 3 = 14 - 5w

add 5w to each side of the equation:

11w + 3 = 14

subtract 3 from each side:

11w = 11

divide both sides by 11:

w = 1

please help! it’s 9:00 and i just want to be done...

Answers

Answer:

Step-by-step explanation:

1. 3/7

2. 1/5

3. 7 and 21

Answer:

1) 3/4

2) 1/5

3) 7 and 21

4) 9 tokens a day

5) 6 laps a week

Which shape represents the cross section formed by the plane

Answers

Answer:

triangle

Step-by-step explanation:

m- 0.3 > 1.45
Answer?

Answers

Answer:

[tex]m > 1.75[/tex]

Step-by-step explanation:

1) Add 0.3 to both sides.

[tex]m > 1.45 + 0.3[/tex]

2) Simplify 1.45 + 0.3 to 1.75.

[tex]m > 1.75[/tex]

Therefor, the answer is m > 1.75.

i need this done today whoever gets it correct gets brainliest!! PLZZZ HELPPP MEEE

Answers

Answer:

9x+6

Step-by-step explanation:

help plz!!!!!!!!!!!!!!!!!!!!!

Answers

Answer: D

Explanation:

A dessert recipe calls for 2 1/2 cups of milk and makes 5 servings. How many cups of ilk are needed for 8 servings?

Answers

Answer:

4 cups

Step-by-step explanation:

Number of cups of milk for 5 servings = [tex]2\frac{1}{2} =\frac{5}{2}[/tex] cups

First find number of cups of milk for 1 serving.

Number of cups of milk for 1 serving = [tex]\frac{\frac{5}{2} }{5}=\frac{1}{2}[/tex] cup

Now find umber of cups of milk for 8 servings.

Therefore,

Number of cups of milk for 8 servings = [tex]8(\frac{1}{2})=4[/tex] cups

.
P(x) is a polynomial.
P(x) divided by (x – 8) has a remainder of 5.
P(x) divided by (x – 5) has a remainder of 3.
P(x) divided by (x + 5) has a remainder of -2.
P(x) divided by (x + 8) has a remainder of 0.
Find the following values of P(x).
P(5) =
P(-8) =

Answers

Answer:

x-5 = 0 has a remainder of 3

x = 5

therefore p(5) = 3

x+8 = 0 has a remainder of 0

x = -8

therefore p(-8) = 0

Two angles are shown. K is 7 times as large as L. The angles are complementary. What is the measurement in degrees for K

Answers

Answer:

∠K = 78.75°

Step-by-step explanation:

since complimentary, ∠K + ∠L = 90°

K = 7L

substitute for K:

7L + L = 90

8L = 90

∠L = 11.25°

∠K = 90° - 11.25° = 78.75°

can you show me step by step how to do this 7.34 x 0.6

Answers

Answer:4.404

Step-by-step explanation: All you have to do is place it in standard algorithm, and you start multiplying

Answer:

= 4.404

Step-by-step explanation:

= 7.34 × 0.6

Remove the point

= 734 × 6

= 4 404

Then shift the point for 3 times

:. = 4.404

Pls help me guys I have no clue how to do it!!!!

Answers

Answer:

234 mm²

Step-by-step explanation:

area of each side = L x W

(15 x 3 x 2) + (15 x 4 x 2) +(3 x 4 x 2) = 234 mm²

what is the y intercept of the linear function graphed here​

Answers

The y-intercept is (0,-1)

Answer:

0,-1

Step-by-step explanation:

Please can someone give me correct answer to this problem.
I will mark you brainliest for the correct answer.
Please help!!!!!!!!!!!!!!!!!!!

Answers

The answer is C or D but I would do D

While waiting for a video game to download, you notice that 30\%30%30, percent of 32{,}00032,00032, comma, 000 kilobytes have been downloaded so far.

Answers

Answer is in the file below

tinyurl.com/wpazsebu

Answer:

9600 kilobytes

Step-by-step explanation:

"of" means to multiply, so 0.3 times 32000 is 9600

who the hell gave conan gray the right to looke this fine like i- anyways look at hiiiiiim

Answers

Answer:

very cute

Step-by-step explanation:

Ian even know him until now but he mad fine

HHHHHHHHHEEEEEEEEEELLLLLLLLLLPPPPPPPPP ILL FAIL MY CLASSSSSSSSSSSSSS
for number 4 because it has select, the select are


first one under C) 66, 64, 67, 65

under B) 24, 23, 26, 25

under A) 15, 16, 17, 18

lowest under C) 40, 41, 42, 39

Answers

Answer:

c is the right answer of this

Answer:

The first blank: 65

The second blank: 24

The third blank: 16

The last blank is: 41

Step-by-step explanation:

The Phthagorean theorm is as follows: c^2=a^2+b^2

Where a and b are the legs of the triangle and c is the hypotenuse

To fill in the first blank space you need to find c, and it's given a and b: a=25 b=60

You substitute the known values into the equation of the Pythagorean theorm: c^2=25^2+60^2

And solve to find c

c^2=4225

c=

[tex] \sqrt{4225} [/tex]

c=65

The answer for the first blank

For the second blank you given a and c: a=7 c=25

Substitute the value into Pythagorean theorm:c^2=a^2+b^2

25^5=7^2+b^2

625=49+b^2

To solve b you got to subtract 49 to both sides

625-49=b^2

576=b^2

[tex] \sqrt{576} = b[/tex]

24=b

Which is your answer

For the third blank its given b and c: b=30 c=34

Substitute the value into Pythagorean theorm

c^2=a^2+b^2

34^2=a^2+30^2

Solve the exponential terms: 1156=a^2+900

Then you solve the variable that you need to find. In this case, you got to solve a^2 by subtracting 900 of both sides of the equation:1156-900=a^2

256=a^2

[tex] \sqrt{256 = a} [/tex]

16=a which is your answer

Finally your last blank,its given the values and b

a=9

b=40

Substitute the value into Pythagorean theorm

c^2=9^2+40^2

And solve for c

c^2=81+1600

c^2=1681

[tex]c = \sqrt{1681} [/tex]

Which gives you c=41 which is your answer

Let me know if this helps

Make t the subject of 5(t − g) = 2t + 7

Answers

Answer:

[tex]5(t - g) = 2t + 7 \\ 5t - 5g = 2t + 7 \\ 5t - 2t = 7 + 5g \\ 3t = 7 + 5g \\ t = \frac{7 + 5g}{3} [/tex]

No need for explanation

Answers

Answer:

32

Step-by-step explanation:

I'll assume they're vertical angles

5x - 13 = 2x + 14

3x = 27

x = 9

<ABC:

5x - 13

5(9) - 13

32

Answer:

L.49

NO EXPLANATION

sin A =

option 1: 40/9

option 2: 9/41

option 3: 40/41

option 4: 41/40

what is the correct answer?

Answers

Answer: Option 3 40/41

Step-by-step explanation:

Sin of angle A means the opposite over hypotenuse. The opposite of Angle A is 40 and the hypotenuse is 41 so SinA is 40/41

Answer:

option 3:  [tex]\frac{40}{41}[/tex]

Step-by-step explanation:

SOH CAH TOA

sine = [tex]\frac{opposite}{hypotenuse}[/tex]

sine A = [tex]\frac{40}{41}[/tex]

does anyone have all the answers to the 8th grade math DRC interim for vermillion parish. bc I'm here stuck pls help. session 1 ​

Answers

You can download answer here

is.gd/qKzpBU

Answer:

I think I might have them from last year?

Step-by-step explanation:

Otero translated the phrase "three less than a number" into the expression 3 minus x. Which best describes the accuracy of Otero's expression?

Answers

Correct Question:

Otero translated the phrase "three less than a number" into the expression 3 minus x. Which best describes the accuracy of Otero's expression?.

a. It is accurate. The phrase can be translated as "three" = 3, "less than" = subtraction, and "a number" = X, SO 3- X is the correct expression.

b. It is inaccurate. Three is being subtracted from a number, so X-3 is what he should have written.

c. It is inaccurate. Three is being compared to a number, so 3 It is inaccurate. Three is being added to a number, so 3+ x is what he should have written.

Answer:

The answer is B because three less than a number means that a 3 is less than some number X meaning three is being subtracted from X. So equation should be X-3 rather than 3-X.

Step-by-step explanation:

Answer:

The answer is c i just took this test lol

Step-by-step explanation:

have a good day :)

What is the value of c ?

Answers

Answer:

34

Step-by-step explanation:

:)

Answer:

34

Step-by-step explanation:

Remember that the sum of the angles of a triangle is 180

And since two sides are congruent b = 73

So 180-(73+73) = 34

calculate the diameter of the circle

Answers

Answer:

2.64cm

Step-by-step explanation:

A = π r^2

5.5 = π r^2

1.75 = r^2

r = 1.32

Diameter is then 2(1.32) = 2.64

Answer:

2.65 cm to the nearest hundredth

Step-by-step explanation:

A = πr^2 = 5.5

r^2 = 5.5/ π = 1.5707

r = 1.3231

Diameter = 2 * r

= 2.6462.

The hypotenuse of an isosceles right triangle is centimeters longer than either of its legs. Find the exact length of each side.​ (Hint: An isosceles right triangle is a right triangle whose legs are the same​ length.)

Answers

Question

The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.

Answer:

[tex]Hypotenuse:37.56[/tex]

[tex]Other\ Legs: 26.56[/tex]

Step-by-step explanation:

Let the hypotenuse be y and the other legs be x.

So:

[tex]y = 11 + x[/tex]

Required

Determine the exact dimension of the triangle

Using Pythagoras theorem;

[tex]y^2 = x^2 + x^2[/tex]

[tex]y^2 = 2x^2[/tex]

This gives:

[tex](11+x)^2 = 2x^2[/tex]

Open bracket

[tex]121 + 22x + x^2= 2x^2[/tex]

Collect like terms

[tex]2x^2 - x^2 -22x - 121 = 0[/tex]

[tex]x^2 -22x - 121 = 0[/tex]

Using quadratic formula:

[tex]x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]x = \frac{-(-22)\±\sqrt{(-22)^2 - 4*1*-121}}{2*1}[/tex]

[tex]x = \frac{-(-22)\±\sqrt{968}}{2*1}[/tex]

[tex]x = \frac{22\±31.11}{2}[/tex]

Split

[tex]x = \frac{22+31.11}{2}\ or\ x = \frac{22-31.11}{2}\\[/tex]

[tex]x = \frac{53.11}{2}\ or\ x = \frac{-9.11}{2}[/tex]

x can not be negative.

So:

[tex]x = \frac{53.11}{2}[/tex]

[tex]x = 26.56[/tex]

Recall that:

[tex]y = 11 + x[/tex]

[tex]y = 11 + 26.56[/tex]

[tex]y = 37.56[/tex]

Hence, the dimensions are:

[tex]Hypotenuse:37.56[/tex]

[tex]Other\ Legs: 26.56[/tex]

Gabriela has an average daily balance of $232.94 on her credit card. Her card charges 9.25% annual interest. What will her monthly finance charge be?
$9.25
$21.60
$1.80
$0.78

Answers

Answer:

Step-by-step explanation:

B

Answer:

C

Step-by-step explanation:

$232.94 * 9.25% = 21.54694

21.54694 rounds up to 21.55

21.55/12 = 1.7958333333

1.7958333333 rounds up to 1.80

------------------------------------------------------------

This is a late answer but other people might need it :)

I put B as my answer and I got it wrong, I tried again and put C and got it right.

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