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Michelle deposited $1,600 into an account that is compounded continuously with an annual interest rate of 8%. After t years, there was $3,200 in the account. Based on the given information, if the formula for continuously compounded interest is A = P e r t , where P represents the initial amount of money, r represents the annual interest rate (as a decimal), t represents the number of years, and A represents the amount of money after t years, how many years had the money been in the account? Express your answer as a logarithm.
Answers
Answer:
As a logarithm, the money had been in the account for [tex]t = \frac{\ln{2}}{0.08}[/tex] years.
Step-by-step explanation:
The amount of money in the account after t years is given by:
[tex]A(t) = Pe^{rt}[/tex]
In which P is the initial amount deposited and r is the interest rate, as a decimal.
Michelle deposited $1,600 into an account that is compounded continuously with an annual interest rate of 8%.
This means that [tex]P = 1600, r = 0.08[/tex]
After t years, there was $3,200 in the account. How many years had the money been in the account?
This is t for which [tex]P(t) = 3200[/tex]. So
[tex]A(t) = Pe^{rt}[/tex]
[tex]3200 = 1600e^{0.08t}[/tex]
[tex]e^{0.08t} = \frac{3200}{1600}[/tex]
[tex]e^{0.08t} = 2[/tex]
[tex]\ln{e^{0.08t}} = \ln{2}[/tex]
[tex]0.08t = \ln{2}[/tex]
[tex]t = \frac{\ln{2}}{0.08}[/tex]
[tex]t = 8.67[/tex]
As a logarithm, the money had been in the account for [tex]t = \frac{\ln{2}}{0.08}[/tex] years.
The value of time t is [tex]\frac{ln(2)}{0.08}[/tex].
Given: P=1600
r=8%=0.08
t = ?
A=3200
Using the given compound interest formula we get:
[tex]A=Pe^{rt}\\3200=1600e^{0.08t}\\2=e^{0.08t}\\[/tex]
Take ln on both sides,
[tex]ln(2)=ln(e^{0.08t})\\ln(2)=0.08t\\t=\frac{ln(2)}{0.08}[/tex]
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What is the volume of a cube with edge lengths of 2/3 units
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Answer:
Step-by-step explanation:
8/27 because if you think about it 2/3 x 2/3 x 2/3 x 2/3 = 8/27
Joshua wants to buy sport shoe cost P435.30 if he saved from his allowance a total of P289.75 how much does he still need to buy the shoe
Answers
Answer:
P 145.55
Step-by-step explanation:
435.30 - 289.75 = 145 .55
NEED IMMEDIATE HELP I DIDNT GET ANYTHING THE TEACHER TAUGHT ME TODAY! Can someone please answer all my questions? I would really appreciate it! I need to get my math grade up. :)
To see my questions download the PDF and you can answer all of them for me. :)))))
Answers
Answer:
Step-by-step explanation:
In similar triangles, the corresponding sides will be in same ratio
[tex]2) \frac{x}{8}=\frac{30}{15}\\\\x =\frac{30}{15}*8\\\\x=2*8\\\x = 16[/tex]
[tex]3) \frac{x}{20}=\frac{12.8}{16}\\\\x = \frac{12.8}{16}*20\\\\x= \frac{128}{8}\\\\x = 16[/tex]
[tex]\frac{y}{10}=\frac{12.8}{16}\\\\y=\frac{12.8}{16}*10\\\\\\y=8[/tex]
[tex]4) \frac{x}{15}=\frac{8}{6.4}\\\\x=\frac{8}{6.4}*15\\x=18.75[/tex]
[tex]5) \frac{x}{12}=\frac{22.5}{9}\\\\x=\frac{22.5*12}{9}\\\\x= 30[/tex]
[tex]6)\frac{14}{8}=\frac{7}{4}\\\\\frac{12}{6}=\frac{2}{1}\\\\\frac{10}{5}=\frac{2}{1}[/tex]
As the ratio of corresponding sides are not proportion, these are not similar triangles
What are the solutions to the equation (m + 1)2 +1 = 5? (1 point)
m = 3 or m = -5
m = 1
m = l or m = -3
m = -3
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Answer:
yes c is correct ... go on keep going
BEST OF LUCK
Which of the following circles has the greatest circumference? Use 3.14 for the pi.
A circle with radius 4 meters
A circle with diameter 7 meters
A circle with circumference 24 meters
A circle with circumference 5 pi
Answers
Answer:
24 m
Step-by-step explanation:
it is 24metre ok......
The greatest circumference is 25.12 meters.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The area of a circle is πr².
We have,
A circle with a radius of 4 meters.
Circumference.
= 2πr
= 2 x 3.14 x 4
= 25.12 meters
A circle with a diameter of 7 meters
Radius = 7/2 meters
Circumference.
= 2πr
= 2 x 3.14 x 7/2
= 21.98 meters.
A circle with a circumference of 24 meters
Circumference = 24 meters
A circle with a circumference of 5 pi
Circumference = 5π
= 5 x 3.14
= 15.7 meters
Thus,
The greatest circumference is 25.12 meters.
Learn more about circle here:
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17 is between which two integers ?
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Answer:
Step-by-step explanation:
two integers mean numbers that do not have decimals. Whole numbers
to figure out between what two integers get a calculator
which is 4.123 (to three decimal places)
thus it falls between 4 and 5. since it is above 4 and below 5 and there are no integers in between possible.
- brainly user
HELP...... rewrite the equation by completing the square.
x ^2 +10x+16=0
Answers
Answer:
[tex](x+5)^{2} = 9[/tex]
Step-by-step explanation:
To complete the square you need to add [tex]\frac{b}{2}^{2}[/tex]to both sides. (Parenthesis around b/2)
b = 10
b/2 = 5
(b/2)^2 = 25
[tex]x^{2}[/tex] +10x + 16 = 0
subtract 16 to both sides
[tex]x^{2}[/tex] + 10x = -16
add 25 to both sides
[tex]x^{2}[/tex] +10x + 25 = 9
Perfect Square Trinomial Factoring
[tex](x+5)^{2}[/tex] = 9
Target buys video games for $25/game. They markup the price by 75%. How much do
they charge customers for a videogame? Do not enter a dollar symbol with your
answer.
Answers
9514 1404 393
Answer:
$43.75
Step-by-step explanation:
The amount of the markup is ...
$25 × 0.75 = $18.75
The final cost to the customer is ...
selling price = purchase price + markup
= $25.00 + 18.75 = $43.75
They charge customers $43.75 for a videogame.
plases helpppppppppppppppppp
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Hope this helps!
mr Ethan divide the a land that measures 42m by 60m into equal what should be the size of largest square
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Find the factors of 42 using the listing method.
42 - 1, 2, 3, 6, 7, 14, 21, 42
Find the factors of 60 using the listing method also.
60 - 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Identify the common factors of 42 and 60.
42 - 1, 2, 3, 6, 7, 14, 21, 42
60 - 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Common Factors: 1, 2, 3, 6
Therefore, the size of the largest square is 36m² since 6m x 6m is equals to 36m².
About 16% of people who get their feet examined are found to have athlete's foot. What is the probability of a podiatrist examining five people until he finds the first patient who has athlete's foot? (0.16)^5 (0.84)^4(0.16)^1 (0.16)^4(0.84)^1 (0.84)5 1 − (0.16)^4
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Answer:
Step-by-step explanation:
(84/100)^4(16/100)
(0.84)^4(0.16)^1
Help pls!!! Worth 16 points!!!:)))
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Answer:
18: Safe volume: s <= 115. Unsafe: s > 115.
19: 2-a, 1-b, 3-c, 4-d
20a: Justin is incorrect. 12 is a solution. 12 >= 12 is a true statement.
20b: f > 12
Step-by-step explanation:
PLZ ANSWER QUICKLY! POINTTTSSS POINTTTSS! THX
If f(x) = 3(x + 4), find f(2).
729
243
81
18
Answers
Answer:
18
Step-by-step explanation:
We just substitute x
3(2+4)=6+12=18
For a dilation with a scale factor less than 1, how do the angles and side lengths of the preimage relate to the angles and side lengths of the image?
A. Angle are proportional;side lengths are larger
B. Angles are proportional;side lengths are smaller
C. Angles are congruent;side lengths are larger
D. Angles are congruent; side lengths are smaller
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The dilation of an image with a scale factor less than 1 will have the angle proportional to the preimage, and the side lengths have been smaller. Thus, option B) is correct.
The dilation factor has been the scale factor that has been used for the enlargement or reduction of the image. The images with a dilation factor of more than 1 enlarge, while the images with a dilation factor less than 1 shrinks.
The angle of the image with a scale factor less than 1 has been proportional as with shrinking, the angles have been reduced proportionally with the scale factor.
The reduction in scale factor from 1 will shrink the image. The shrinked image will be consist of a smaller size. So there has been a reduction in the side length of the image.
So, with the image with dilation of scale factor less than 1, the angles are proportional while the side length is smaller. Thus option B) is correct.
For more information, refer to the link given below:
https://brainly.com/question/17267403
Please help me out here, I’ve been reposting the same questions and have not seen people not answer mine. :( just please i will give u brainiest
Answers
Answer:
There are infinite solutions because they are the same equation
2D + 1G = 12
and
4D + 2G = 24 (divide by 2) 2D + G = 12
2D + 1G = 12 is the same as 2D + 1G = 12
A number divided by eight minus thirteen is greater than negative six.
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Answer:
(x/8) - 13 > -6
Step-by-step explanation:
If you want to take it further, add 13 to both sides to make it x/8 > 7. Then divide both sides by 8 to get x by itself. you are left with x > 7/8
Random tip to remember: when dividing by negatives, remember to switch the inequality signs (this is just for future reference)
What's 16/12 + 11/6?
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Answer:
It's 3 1/6 :) I hope it helps
please help me.......
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Subtract 4 from 1/6 of 42
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Answer:
3 is the answer
Step-by-step explanation:
1/6 of 42 is 7, 7-4=3
You can search it up if you think I am wrong
Answer:
-3 is the correct answer
In a survey of 1090 investors, it was determined that 690 invested in stocks, 575 in bonds and 300 in both stocks and bonds.
a. How many invested in only stocks?
b. How many invested in stocks or bonds?
c. How many did not invest in either stocks or bonds
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something is wrong with your question bc 690 plus 575 equals to 1265
quater of 80? its for my maths, thanks xx
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explanation
20*4= 80
hope i helped!
Quarter of 80:
= 80 x 1/4
= 80/4
= 20
Sam received his monthly credit card statement. He was shocked to find a debit transaction of $2,799 for a smart watch that he hadn’t purchased. He noticed that the fraudulent transaction had been made just a couple of days ago. He was aware that the card had been missing for a several months, but he had forgotten to inform the credit card company about the lost card. What’s the maximum amount sam will have to pay for this fraudulent transaction?
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Answer:
The entire amount
Step-by-step explanation:
Sam will have to incur the amount of the transaction performed, this is because the transaction occurred using his credit card and he also attested to the fact that the card was missing for several month. After losing his credit card, Sam should have informed the credit card company about the development so that necessary steps could be taken, which he failed to do. For these, reason, Sam will have to bear the loss and pay the credit card company the entire sum.
Answer:
Fair credit billing act and the full amount is correct on plato.
Step-by-step explanation:
Name 6 elements of PQR.
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Answer:
josh
rabeesh
ronger
roger
roge
robert
Step-by-step explanation:
7.5d=2.5d, lin divides each side by 2.5d, and elena subtracts 2.5d from each side
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Answer:
2.5d is your answer right answer
SOMEONE HELP PLZZZ ASAP
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So it would be (2x-1)^4
Which is equivalent to (2x-1) (2x-1) (2x-1) (2x-1)
Whenever you do foil and simplify, you get -
16x^4 - 32x^3 + 24x^2 - 8x + 1
(Could I have my first brainliest?)
Answer:
Answer:
(2x−1)(2x−1)(2x−1)(2x−1)
Step-by-step explanation:
Factor 16x4−32x3+24x2−8x+1
16x4−32x3+24x2−8x+1
=(2x−1)(2x−1)(2x−1)(2x−1)
The point (3 , k) is a distance of 5 units from (0 , 1). Find the two possible values of k.
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......._____________
5 =√(3-0)^2 + (k-1)^2
.......__________
5 =√3^2 + (k-1)^2
25 = 9 + (k-1)^2
16 = k^2 - 2k + 1
k^2 -2k - 15 = 0
(k - 5)(k + 3) = 0
k - 5 = 0.....or.......(k + 3) = 0
k = 5.........or.......k = -3
I need help with this
look at picture
Complementary angles
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Answer:
x is equal to 11...........
90°-35°= 55°
Mark as brainlist
I really need help plz
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Answerwhat do you need help with?
Step-by-step explanation:
PLZ help me with this question
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Answer:
I believe it's A and D.
If I helped you're welcome. If I didn't I'm sorry.
Answer:
A and D
Step-by-step explanation:
im not too good on fractions but hopefully its right
