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
11111nata11111 [884]
2 years ago
14

A huge ice glacier in the Himalayas initially covered an area of 454545 square kilometers. Because of changing weather patterns,

this glacier begins to melt, and the area it covers begins to decrease exponentially.
The relationship between AAA, the area of the glacier in square kilometers, and ttt, the number of years the glacier has been melting, is modeled by the following equation.
A=45e^{-0.05t}A=45e
−0.05t
A, equals, 45, e, start superscript, minus, 0, point, 05, t, end superscript
How many years will it take for the area of the glacier to decrease to 151515 square kilometers?
Give an exact answer expressed as a natural logarithm
Mathematics
1 answer:
guajiro [1.7K]2 years ago
6 0

We have been given that a huge ice glacier in the Himalayas initially covered an area of 45 square kilo-meters. The relationship between A, the area of the glacier in square kilo-meters, and t, the number of years the glacier has been melting, is modeled by the equation A=45e^{-0.05t}.

To find the time it will take for the area of the glacier to decrease to 15 square kilo-meters, we will equate A=15 and solve for t as:

15=45e^{-0.05t}

\frac{15}{45}=\frac{45e^{-0.05t}}{45}

\frac{1}{3}=e^{-0.05t}

Now we will switch sides:

e^{-0.05t}=\frac{1}{3}

Let us take natural log on both sides of equation.

\text{ln}(e^{-0.05t})=\text{ln}(\frac{1}{3})

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

-0.05t\cdot \text{ln}(e)=\text{ln}(\frac{1}{3})

-0.05t\cdot (1)=\text{ln}(\frac{1}{3})

-0.05t=\text{ln}(\frac{1}{3})

t=\frac{\text{ln}(\frac{1}{3})}{-0.05}

t=\frac{\text{ln}(\frac{1}{3})\cdot 100}{-0.05\cdot 100}

t=\frac{\text{ln}(\frac{1}{3})\cdot 100}{-5}

t=-\text{ln}(\frac{1}{3})\cdot 20

t=-(\text{ln}(1)-\text{ln}(3))\cdot 20

t=-(0-\text{ln}(3))\cdot 20

t=20\text{ln}(3)

Therefore, it will take 20\text{ln}(3) years for area of the glacier to decrease to 15 square kilo-meters.

You might be interested in
Ten times the sum of half a number and 6 is 8.
Sedaia [141]
That would be 

10( \frac{1}{2} n + 6) = 8
\frac{1}{2} n+6= \frac{8}{10}
.5n + 6 = .8
.5n = -5.2
n=-2.6

Hope that helps :)
8 0
3 years ago
What is the answer?​
krek1111 [17]

Answer:

the answer should be always, which would be b

Step-by-step explanation:

if you have a reciprocal 3/2 then the fraction would be 2/3 which is proper. you just flip the numbers.

5 0
3 years ago
a triangle has a 40° angle, a 120° angle and a side 2.5 centimeters in length. which of the following statements are true about
pochemuha

Answer:

C

Step-by-step explanation:

A triangle is 180 degrees so 120+40 is 160

180-160=20

6 0
2 years ago
3 2/5 + 9 1/10= Simplest form
Talja [164]

Change each mixed fraction to improper

3 2/5 = 15/5 + 2/5 = 17/5

9 1/10 = 90/10 + 1/10 = 91/10

Find a common denominator. Multiply 2 to both numerator and denominator of 17/5

17/5(2/2) = 34/10

34/10 + 91/10 = 125/10

125/10

Simplify. Divide

125/10 = 12.5

12.5 is your answer

hope this helps

3 0
2 years ago
Read 2 more answers
What is 75% of 240? I'll love you if you give me an answer
Delicious77 [7]
180................................l.
6 0
2 years ago
Other questions:
  • Two containers filled with water are leaking. Container A leaks at a rate of 1/4 gallon per hour. Container B leaks at a rate of
    9·1 answer
  • Anyone understand this???
    5·2 answers
  • A and B share the cost in a ratio of 3:2. A pays £125 how much does b pay?
    15·2 answers
  • How do you divide fractions
    8·1 answer
  • I am thinking of three positive numbers. The mode is 5 The median is 5 The range is 9 Work out the three numbers.
    11·1 answer
  • Camille's kitchen has an area of 80 square feet. The kitchen is 8 times as many square feet as Camille's pantry. If the pantry i
    5·1 answer
  • Jared had 5 chocolate bars left over from Halloween. During a party with 5 of his other friends, they shared the chocolate bars.
    7·1 answer
  • If we have a square with an area of 75 square meters, what would the side length be?
    12·2 answers
  • Last month we had only five sunny days. There were 30 days in all last month.
    14·2 answers
  • Algebraic models grade 12 math college please write the answers without explaining thank you.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!