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

Simplify:<br><br><br> 2+5(x+3)- (2x-7)(x+2)<br><br> PLEASE SHOW WORK!!!

svetoff [14.1K]

Answer:

2+5(x+3)- (2x-7)(x+2)

7(x+3)- (3x+4x-7x-14)

(7x+21)-(7x-7x-14)

(7x+21)-(14)

7x+21-14

=7x+7

<h2><em>Please mark as brainliest answer!!!!</em></h2>

4 0

2 years ago

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Please answer it if it is true i will make you the brainliest.

Firlakuza [10]

The answer I got was 2c-48 still trying to figure out the matching part

6 0

2 years ago

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Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves

Radda [10]

A washer has outer radius $2-x^2$ and inner radius $2 - \sqrt{x}$

$\displaystyle V = \int_0^1 \pi\Big[ \left( 2 - x^2 \right)^2 - \left( 2 - \sqrt{x}\right)^2\Big] dx$

4 0

3 years ago