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 1

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.

Answer 2

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]

Learn more: https://brainly.com/question/12325365


Related Questions

a department store sells a pair of shoes with an 87% markup, if the store bought the pair of shoes for 55.25, what is the selling price to the nearest dollar?

Answers

Answer:

$103

so 87% of $55.25 is 48.0675

48.0675+55.25 is 103.3175

103.3175 rounded to the nearest dollar is 103.

f(x)=-12x^3-14x^2+6x

Answers

There has to be x equals of f is something or u can’t solve

a) Simplify
X - 2 / 7(x - 2)2

Answers

This is what I got. Hope it helps :)

Answer:

3x/7 + 8/7

Step-by-step explanation:

Please help ASAP!
Thank you

Answers

The answer has to be 16 because when you add them it goes up
Yep. Your answer would be 16

piete)
Decide whether the following statement makes sense or does not make sense. Explain your reasoning.
I drove at a speed of 35 miles for the entire trip.

Answers

Answer:

It doesn't make sense

Step-by-step explanation:

Given

Statement: .... at a speed of 35 miles .....

Required

Does it make sense?

In motion, speed is measured in km/h, m/s, miles per hour (depending on context) while distance is measured in km, m or miles.

However, the given statement mention the unit of speed to be miles which is incorrect.

Hence, we can conclude that the statement does not make sense.

A correct statement would be: I drove at a speed of 35 miles per hour .......

Pleas e help me 100 points and brainliest

Answers

Answer:

this is your answer. I think it is right.

Answer:

see the answers

Step-by-step explanation:

to understand thisyou need to know about:factoringlCDPEMDAStips and formulas:L.C.D=lowest common denominatorlet's solve:

[tex]1) \sf\frac{7}{m - 6} \: , \frac{1}{m} \\ [/tex]

denominators are m-6,m

therefore

the lowest common denominator is

(m-6)(m)

[tex] \sf\frac{1}{n - 1} \: , \frac{1}{ {n}^{2} - 2n + 1 } [/tex]

denominators n-1,n²-2n+1

step-1

factor n²-2n+1 to find the lowest common denominator

use (a-b)²=a²-2ab+b to factor n²-2n+1

therefore

(n)²-2.n.1+(1)²(n-1)²

therefore

the L.C.D of the second expression is

(n-1)² alternative form(n-1)(n-1)

[tex]3) \tt\frac{k}{ {h }^{2} - 5h + 6} \: , \frac{3}{h -3 } [/tex]

step-1

factor out h²-5h+6 to find L.C.D

rewrite -5h as -2h-3h: h²-2h-3h+6factor out h: h(h-2)-3h+6factor out -3: h(h-2)-3(h-2)group: (h-3)(h-2)

therefore

the L.C.D of the third expression is

(h-3)(h-2)

Write a rule for a function with a parabolic graph that contains the x-intercepts (-20,0) and (40,0) and a maximum point whose y-coordinate is 30.

Answers

Step-by-step explanation:

Since the x-intercepts are -20 and 40, the line of symmetry is x = (-20 + 40)/2 = 10.

Now we have y = a(x - 10)² + 30, where a is an unknown constant. We can find a by using an x-intercept point.

=> (0) = a[(40) - 10]² + 30

=> 900a + 30 = 0, a = -1/30.

Hence the rule is y = -(x - 10)²/30 + 30.

Suppose you know that ∠S and ∠Y are complementary, and that m∠S = 4(m∠Y) − 210°. Find m∠Y.

Answers

Answer:

angle Y= 60 degrees

Step-by-step explanation:

angle S + angle Y = 90 degrees because they are complementary

Y = 90 - S

angle S = 4(Y)-210

substitute for Y

S = 4(90 - S) - 210

S = 360 - 4S - 210

reduce

5S = 150

S = 30

Y = 90 - 30 = 60

Simplify completely*****​

Answers

Answer:

[tex]\displaystyle \frac{2(x + 4)}{3}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Terms/CoefficientsFactoring

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \frac{4x + 16}{6}[/tex]

Step 2: Simplify

[Fraction] Factor numerator:                                                                           [tex]\displaystyle \frac{4(x + 4)}{6}[/tex][Fraction] Reduce:                                                                                          [tex]\displaystyle \frac{2(x + 4)}{3}[/tex]

One winter day, the temperature in Houston is 8 Celsius. Find the temperatures in these other cities. Explain or show your reasoning.
In Orlando, it is 17 warmer than it is in Houston
In Salt Lake City, it is 18 colder than it is in Houston
In Minneapolis, it is 25 colder than it is in Houston
In Fairbanks, it is 12 colder than it is in Minneapolis
Write an addition equation that represents the relationship between the temperature in Houston and the temperature in Fairbanks.

Answers

Orlando = 25° because 17+8
Salt Lake city = -10° because 8-18
Minneapolis = -17° because 8-25
Fairbanks = -29° because -17-12

Houston = 8° - 37° = Fairbanks

Hence, the temperatures in these other cities are

Orlando is [tex]25[/tex] degree

Salt Lake is [tex]-10[/tex] degree

Minneapolis is [tex]-17[/tex] degree

Fairbanks is [tex]-29[/tex] degree

What is the degree?

A degree, usually denoted by °, is a measurement of a plane angle in which one full rotation is [tex]360[/tex] degrees.

Here given that,

One winter day, the temperature in Houston is [tex]8[/tex] Celsius.

In Orlando, it is [tex]17[/tex] warmer than it is in Houston.

In Salt Lake City, it is [tex]18[/tex] colder than it is in Houston.

In Minneapolis, it is [tex]25[/tex] colder than it is in Houston.

In Fairbanks, it is [tex]12[/tex] colder than it is in Minneapolis.

So, it would be

Orlando = [tex]25[/tex] degree

because [tex]17+8=25[/tex] degree

Salt Lake city [tex]= -10[/tex] degree

because [tex]8-18=-10[/tex] degree

Minneapolis [tex]= -17[/tex] degree

because [tex]8-25=-17[/tex] degree

Fairbanks [tex]= -29[/tex] degree

because [tex]-17-12=-29[/tex] degree

Hence, the temperatures in these other cities are

Orlando is [tex]25[/tex] degree

Salt Lake is [tex]-10[/tex] degree

Minneapolis is [tex]-17[/tex] degree

Fairbanks is [tex]-29[/tex] degree

To know more about the  degree

https://brainly.com/question/15652682

#SPJ2

how many inches is 2 1/6 ft​

Answers

Answer:

26 inches

Step-by-step explanation:

The answer is 26 inches

whats 8 x 2 40 points

Answers

Answer:

Error hehehheheheh

Step-by-step explanation:

crown me please hehehhhe hahahahahh hohohoohoho points more more more more points

Help me please!!
15 points!

Answers

Answer:

Hi Hi really sorry may i get some points i need them to give it to other people cuz some people want points, ik its not the answer u wanted sorry but hope u get the answer soon!

Step-by-step explanation:

Lillian wants to give 1/3 of a pizza to each of six girls at her party. Dragon drop the correct equation an answer to find how many pizzas Lillian needs

Answers

Answer:

2 pizza

Step-by-step explanation:

Given

[tex]Pizza = \frac{1}{3}[/tex]

[tex]Girls = 6[/tex]

Required

Amount of Pizza needed

To do this, we simply multiply the fraction of pizza by the number of girls i.e.

[tex]Amount = Pizza * Girls[/tex]

[tex]Amount = \frac{1}{3} * 6[/tex]

[tex]Amount = 2[/tex]

Hence, Lilian needs 2 pizza

Jeff had 20 $ he spent 1/8 on his money on lunch and 2/5 of his money at the movies. How much money does Jeff have left

Answers

Answer:

9.50$

Step-by-step explanation:

First, multiply 20 by the given fractions

20*1/8=2.5

20*2/5=8

Add the two together to get the total amount of money Jeff spent, 10.5, then subtract 10.5 from 20 to get the total amount he has left, 9.5

Answer:

$9.50

I did a test with this question and the correct answer was 9.50

ou intend to draw a random sample in order to test a hypothesis about an unknown population mean. You will use a hypothesis test. A description of each of the steps of a hypothesis test follows, but they may be specified in the incorrect order. Specify the correct order of the steps. Determine the null and alternative hypotheses. Draw a conclusion about the unknown population using what is known about the sample. Determine the probability at which you will conclude that the sample outcome is very unlikely. Draw a random sample, and calculate the sample statistic.

Answers

Answer:

Determine the null and alternative hypotheses :  STEP 1

Draw a conclusion about the unknown  population using what is known about the sample :  STEP 4

Determine the probability at which you will conclude that the sample outcome is very unlikely :  STEP 2

Draw a random sample and calculate the sample statistic : STEP 3

Step-by-step explanation:

The correct order of the steps are :

Determine the null and alternative hypotheses :  STEP 1

Draw a conclusion about the unknown  population using what is known about the sample :  STEP 4

Determine the probability at which you will conclude that the sample outcome is very unlikely :  STEP 2

Draw a random sample and calculate the sample statistic : STEP 3

2 and 1/8 + 1 and 3/4

Answers

3.875 hope this is right

Pleeeeeeease help me! However helps me first gets brainliest points!

Simplify the following algebraic expressions:
a. - 6x + 5 + 12x -6
b. 2(x - 9) + 6(-x + 2) + 4x
c. 3x2 + 12 + 9x - 20 + 6x2 - x
d. (x + 2)(x + 4) + (x + 5)(-x - 1)
e. (x+8)(x+9)+(x+1)(-x-6)

Answers

Answer:

A) 6x-1

B) -6

C) 9x2+8x-8

D) 3

E) 10x+66

Step-by-step explanation:

There are 30 female performers in a dance recital. The ratio of men to women is 4:5. How many men are in the dance recital?

Answers

men to women ratio is 4:5
females: 30/x = 5
x = 6

males: y/6 = 4
y = 24

there are 24 men in the dance recital.

What is the surface area of the cylinder with height 8 ft and radius 5 ft? Round your answer to the nearest thousandth.

Answers

A≈408.41ft² < that is the answer

What is the volume of a cube with edge lengths of 2/3 units

Answers

8/27 because 2/3*2/3*2/3=8/27

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

how much did he spend on the cookir

Answers

69 69

69 69

69 69 hdgduguedkjeqkd

edhlhiiiiiiiiiiiiiiiiiiiiiii

pppppppppppppppdiepi

e3jdojojejdojeod

A circles radius is 13 meters what is the circles area using 3.14 rounded to the nearest tenth

Answers

Answer:

530.7

Step-by-step explanation:

A circle's area is defined as πr²

You would substitute 13 in for r (the radius) and use 3.14 as your given value for pi, leaving you with this:

3.14×13²

When you calculate this, it should return a value of 530.66, which rounded to the nearest tenth is 530.7

Hope this helps!

If an interest rate of 5% results in interest of $50,
what is the principal amount of the loan?

Answers

X times 0.05 = $50
Solve for x

We do the inverse of times which is divide

$50 divide by 0.05 = $1000

Thus, $1000 is the amount of loan.

Answer:

Ñpswplmlpspapppapapa

Help&EXPLAIN
==============

Answers

Answer:

A = 108 in.²

Step-by-step explanation:

The figure can be decomposed into 3 rectangles.

✔️Area of rectangle 1 = L*W

L = 8 in.

W = 6 in.

Area = 8*6 = 48 in.²

✔️Area of rectangle 2 = L*W

L = 10 in.

W = 4 in.

Area = 10*4 = 40 in.²

✔️Area of rectangle 3 = L*W

L = 5 in.

W = 4 in.

Area = 5*4 = 20 in.

✔️Area of the irregular figure = 48 + 40 + 20 = 108 in.²

Help it’s due today plz

Answers

I can help you with no.1 it is 40

plz help with 24-28!!!!!!!!!!!!!!

Answers

Answer:

4

Step-by-step explanation:

Find The values of ( d ,f ,e ) angles

Answers

Answer:

angle d =35, e=55, f=55.............

(9, 19) (2, 16)
Write the coordinates as decimals or integers.

Answers

Answer:

In decimal 0.428571428

Step-by-step explanation:

The slope = (y2 - y1)/(x2 - x1) y2 = 16, y1 = 19x2=2 and x1=9

The slope = (16 - 19)/(2 -9)

The slope = (-3)/(-7)

The slope = 0.428571428

So in decimal form the coordinates are going to be written as 0.428571428

Slope is the steepness of a line, it is the difference between the y coordinates divided by the difference in x coordinates.

To go on a summer trip, Felipe borrows $200. He makes no payments until the end of 3 years, when he pays off the entire loan. The lender charges sim
Interest at an annual rate of 2%.

Answers

Answer:

Step-by-step explanation:

A=P(1+rt)

A=200(1+.02(3))

A=200(1.06)

A=$212

Other Questions
PLEASE HELP!!Mathematically, when you square root a number, youwill get 2 solutions.Sometimes TrueAlways True Or Never TrueExplain your thinking. Was John Brown a hero? Or a villan? Explain??? \_()_/ Which of these best shows what Raj considers most important? OA. He puts his wife and unborn child before everybody else. B. He does what his mother and father think is best for him. He cares a lot about what others might think of his decisions. OD. He thinks his little brother should learn manners and respect. HHEEELLLPPPP ASAP.... PLS PLS PLS HELP I WILL MARK BRAINLIEST!!!Cells exchange materials with the environment around them. What is the main reason for this?Group of answer choicesA) to replace damaged and dying cellsB) to keep the cell membrane functioningC) to release energy into the environmentD) to get rid of wastes and take in nutrients [HELP! PLEASE] How can you use the double number line diagram to find what percent 240 is of 300? Image is attached, please help asap, thank you, Gracias. Father, I come to you worn and weary from the hard times I have walked through recently. I come to you seeking your shelter where I know I can find security and rest in your shadow. Father, you are mighty. I know my circumstances are no match for Your great power. Father I place a healing of these people that they feel a conviction in there heart that they would turn from there wicked way and turn to you father. IN JESUS NAME AMEN PLEASE PLEASE PLEASE!!! NEED HELP FAST!!! 100 Points!!! REAL ANSWER!!!Calculate the return on investment in dollars and as a percentage for an investment that you purchase for $500 and sell for $600. TIP: if you dont remember how to calculate return on investment, review the Calculating ROI pages in Section 4, Lesson 2. Which of the following best describes the difference between climate and weather Read these excerpts from News Articles about Bullying.Text 1:This week, Jaylen and Mihok will be going into 10 local schools, doing their part to put a stop to bullying."Our presentations are like a pep rally," Robin Arnold said.Text 2:Earlier this month, Jaylen partnered with the Polk County, Florida, school board and local law-enforcement officials to launch a weeklong, countywide anti-bullying initiative . . ."We give out books, wristbands and certificates to the kids and posters and teachers guides to the school, said Robin Arnold.Which detail in Text 1 do you better understand because of details in Text 2?which ten schools Jaylen will visithow Mihok contributes to the presentationswhat Robin Arnold says to the studentswhat Jaylens presentations are like Help plsssssssssss I write it 100 time no one answer plz help with 24-28!!!!!!!!!!!!!! If a rectangle is inscribed in a circle, each diagonal also serves another function. What is this function? 5. There is a bell at the top of a tower that is 45 m high. The bell's mass is 200 kg. The bell has energy. Calculate it.45000900000 J9000 J88200 J Most of the hydrosphere is in what form?freshwaterocean watergroundwaterice 1. The winter weather had everyone wishing it was warmer.AlliterationHyperboleIdiomMetaphorOnomatopoeiaPersonificationSimile I don't get it and I have tried it multiple ways Is Y=-3/4x -2 Y=3/4x+1 One solution many solution or no solution Can software work without Hardware? Why?