Rewrite each of the following expressions without using absolute value. |c| if c<0

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

guajiro [1.7K]

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.

6 0

3 years ago

Tamika made 6 gallons of lemonade. She used 3/4 cup of sugar for each gallon of lemonade, as shown

BARSIC [14]

Answer:

C

Step-by-step explanation:

did da test

6 0

2 years ago

A researcher interested in vocabulary development obtains a sample of twenty 3-year old children to participate in a research st

Andreyy89

Answer: b) statistic

Step-by-step explanation:

Population = A large groups of individuals sharing the same or similar characteristic by the point og study.
Sample = It is a subset of population .
Parameter = It is measure of characteristic in population.
Statistic = It is measure of characteristic in sample.

Since the average score was taken by the group of 20 which is nothing but the sample.

That means, the average score is an example of<u> statistic</u>.

Hence, the correct option is b) statistic .

4 0

2 years ago

In case of an emergency, the office has a calling list so everyone is called in the least amount of time. Each of the first 4 p

svlad2 [7]

Answer:

A.Yes.1st group is nothing ,the 2nd group is nothing,and so on .The 4th group is which does not equal 256 is the correct answer

5 0

3 years ago

What are 25 equations using integers that equal 36?

salantis [7]

36 + 0 = 36, 35 + 1 = 36, 34 + 2 = 36, 33 + 3 = 36, 36 - 0 = 36, 37 - 0 = 36, 38 - 2 = 36, 39 - 3 = 36, 2 + 34 = 36, 4+ 32 = 36, 6 + 30 = 36

8 0

2 years ago