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11111nata11111 [884]
3 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]3 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.

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Answer:

The value of the test statistic is z = -0.877.

Step-by-step explanation:

Testing the difference in mean time spent on housework between husbands and wives.

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The test statistic is:

z = \frac{X - \mu}{s}

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0 is tested at the null hypothesis:

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For the wives the mean was 7 hours/week and for the husbands the mean was 4.5 hours/week. The standard deviation of the differences in time spent on house work was 2.85.

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The value of the test statistic is z = -0.877.

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7 times b reduced by the square of c?
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Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :  

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Step by step solution :

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  -3x + 12  =   -3 • (x - 4)  

Equation at the end of step  1  :

Step  2  :

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Remember to flip the inequality sign:  

Solve Basic Inequality :

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Answer:

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This condition is made the conclusion.

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The acute angle is one in which the value of the angle is less than 90 degrees and obtuse angle is one in which the angle is greater than 90 degrees but less than 180 degrees.

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The conclusion of the given statement  is valid based on the law of detachment as the condition has been made a conclusion.

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