A 200-liter tank initially full of water develops a leak at the bottom. Given that 20% of the water leaks out in the first 5 minutes, find the amount of water left in the tank 10 minutes after the leak develops if the water drains off at a rate that is proportional to the amount of water present.

127.53 liters left after 10 minutes

Step-by-step explanation:

Let

Given

--- initial

--- the amount left, after 5 minutes

Required

--- amount left after 5 minutes

To do this, we make use of:

implies that:

Divide both sides by 200

Take natural logarithm of both sides

So, we have:

Divide by 5

So, the function is:

The amount after 10 minutes is:

answer: b.

step-by-step explanation:

the y coordinate for point b is 0, and answer b is the only one with that y coordinate.

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.