1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ahat [919]
3 years ago
12

For the equation ae^ct=d, solve for the variable t in terms of a,c, and d. Express your answer in terms of the natural logarithm

.
Mathematics
1 answer:
saveliy_v [14]3 years ago
5 0

We have been given an equation ae^{ct}=d. We are asked to solve the equation for t.

First of all, we will divide both sides of equation by a.

\frac{ae^{ct}}{a}=\frac{d}{a}

e^{ct}=\frac{d}{a}

Now we will take natural log on both sides.

\text{ln}(e^{ct})=\text{ln}(\frac{d}{a})

Using natural log property \text{ln}(a^b)=b\cdot \text{ln}(a), we will get:

ct\cdot \text{ln}(e)=\text{ln}(\frac{d}{a})

We know that \text{ln}(e)=1, so we will get:

ct\cdot 1=\text{ln}(\frac{d}{a})

ct=\text{ln}(\frac{d}{a})

Now we will divide both sides by c as:

\frac{ct}{c}=\frac{\text{ln}(\frac{d}{a})}{c}

t=\frac{\text{ln}(\frac{d}{a})}{c}

Therefore, our solution would be t=\frac{\text{ln}(\frac{d}{a})}{c}.

You might be interested in
Joseph served 18 customers in 42 minutes. Approximately how many customers would he serve in 2 hours if he continued at this rat
zhenek [66]
Okay so if he serves 18 customers in 42 minutes divide 18 by 42 and you get the amount of customers he serves per min which is 0.42857413 then multiply that by 120 since 2 hours add up to 120 minutes and you get 51.43
8 0
3 years ago
A marble factory ships marbles using bags of 10, cases of 100, cartons of 1,000, and boxes of 10,000. The factory has an order f
disa [49]
They factory could use 35 cases of 100 and 7 bags of 10.

I hope my answer helps. =)
6 0
3 years ago
Mr. Crow, the head groundskeeper at High Tech Middle School, mows the lawn along the side of the gym. The lawn is rectangular, a
Bogdan [553]

Answer:

Dimensions, Length = 85 feet and Width = 40 feet

Area of lawn = 3400 feet^2

Step-by-step explanation:

Given: Lawn is rectangular in shape

          Length of lawn is 5 feet more than twice its breath/width

           Perimeter of Lawn = 250 feet

To find: (a) Length and width of lawn

             (b) Area of Lawn

First let the a variable for width/breadth. Say, Width = b.

So, the length of lawn = 2b + 5

Perimeter of Rectangle = 2 × ( length + width )

Now, substitue given values in this formula

∴ Perimeter of Lawn = 2 × ( 2b + 5 + b )

250 = 2\times{(2b+b+5)}\\250= 2\times{(3b+5)}\\3b+5 = \frac{250}{2}\\3b = 125 -5\\3b = 120\\b=\frac{120}{3}\\b=40

∴width = 40 feet

⇒ length = 85 feet

Now we find are of lawn using formula of area of rectangle

Area of lawn = length × width

                     = 85 × 40

                     = 3400 feet^2

Dimensions, Length = 85 feet and Width = 40 feet

Area of lawn = 3400 feet^2

7 0
3 years ago
After a 40% discount, the cost of a sofa is $471.00. What was the original cost of the sofa? NEED HELP ASAP
statuscvo [17]

Answer: $659.40

Step-by-step explanation: You start with 471.00 X 0.4 which equals $188.40. So then you add $471.00 and $188.40 and you get $659.40!

5 0
3 years ago
On average, there are 3 pages in every chapter of a James Patterson novel. Each book has approximately 79 chapters. James Patter
sdas [7]

Answer:13746

Step-by-step explanation:

3 * 79 = find amount of pages on average per book

= 237


237 * 58 = find amount of pages written for 58 books

=13746


James Patterson has written approximately 13,746 pages

6 0
3 years ago
Other questions:
  • Angle A B D is a right angle, which is the measure of Angle C B D? Angle A B D is intersected by line C to form angles 75 degree
    13·2 answers
  • I’ve done this before,I’m in 7th rn but I forgot how to do this
    14·2 answers
  • 3 children want to share 2 brownies so that everyone gets the same amount. How much brownie can each child have
    5·2 answers
  • X+ 60 + 120 + 150+ 75 = 360
    8·1 answer
  • Five cat were in a tree. Five more cats go into the same tree. X equals the number of cats in the tree. Anna got X=5, is anna co
    11·1 answer
  • Carys is checking her tax bill for the last year .the tax rates were as follows: no tax on the first 11000 of earnings .earnings
    5·2 answers
  • The price of a jacket was reduced from $30 to $12. By what percentage was the price of the sweater reduced? *
    9·1 answer
  • Will give brainllest and points
    9·2 answers
  • Find the slope of the line passing through the given points<br> (-11,7) and (-11, -2)
    14·2 answers
  • What is the range of h
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!