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
Write the equation of the line that passes through the points (-8,-5) (5,−8)
Nikolay [14]

Answer:

y=-3/13x-89/13

Step-by-step explanation:

m=y²-y¹/x²-x¹

m=(-8)-(-5)/5-(-8)

m=-3/13

y-y=m(x-x1)

y-(-8)=-3/13(x-5)

y+8= -3/13x+15/13

-8 -8

y=-3/13x-89/13

7 0
3 years ago
Show that f(x) = 9x - 2 is a one-to-one function.<br>number​
GREYUIT [131]

Answer:

upon graphing, it is linear

Step-by-step explanation:

you could set up an x-y table or you could graph it

if you graph it you'll see it's linear with a y-intercept of -2 and a slope of 9

all linear equations are functions except for vertical lines

3 0
3 years ago
Can some one helppppppppppp
alexdok [17]

Answer:

66 ft

Step-by-step explanation:

L ∝ n

L = kn , k -> number of sections

Length of 3 sections=  18 ft

3n = 18

 n = 18/3

n = 6 ft

Length of 1 section of fence = 6 ft

Length of 11 sections of fence = 6* 11 = 66 ft

5 0
3 years ago
Read 2 more answers
What is the measure of Y ​
vova2212 [387]

Answer:

62

Step-by-step explanation:

60 + 58 + y = 180

118 + y = 180

y = 180 - 118

y = 62

3 0
2 years ago
Abigail (Abby) Boxer, age 45, is a single mother working as a civilian accountant for the U.S. Army. Her Social Security number
ch4aika [34]

Answer:

Step-by-step explanation:

WHats the question here bud

3 0
3 years ago
Other questions:
  • A bakery uses ounces of icing for every of a cake. What is the unit rate in ounces of icing per cake?
    10·1 answer
  • Find the number of possible positive real zeros of 2x^4+14x^3-35x^2
    9·1 answer
  • The mass of a grain of sand is about 103 gram.
    14·1 answer
  • Frank stands 500 feet from the base of the Statue of Liberty. If Frank looks up with an angle of elevation of 31', how tall is t
    10·1 answer
  • suppose Julie makes 80% of her free throws. what is the probability that she will make 20 of her next 30 attempts? ​
    14·1 answer
  • How do you do question 6
    10·1 answer
  • What is 2 3/12 minus 1 8/12 equal to?​
    9·2 answers
  • The County Fair has to 2 ticket options.Option 1 has an entry fee of $5 and charges $0.65 per ride per ride. Option 2 has an ent
    12·1 answer
  • A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this,
    12·1 answer
  • The diameter of the circle below is 42 cm. Work out the radius of the circle.​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!