A1000 gallon tank, initially full of water, develops a leak at the bottom. given that 300 gallons of water leak out in the first 30 minutes, find the amount of water, a(t), left in the tank t minutes after the leak develops if the water drains off at a rate proportional to the amount of water present.

a. a(t)= 1000(1/3)^1/10t
b. a(t)= 1000(1/2)^-1/10t
c. a(t)= 1000(1001/2)^t
d. a(t)= 1000e ^-1/10t
e. a(t)= 1000(1/2)^1/10t
f. none of these

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

Read the equations in the table below. then drag a description of the situation and a table to represent each equation. indicate whether each of the relationships is proportional or non-proportional.

Find and simplify an expression for the area of five rows of x squares with side lengths of x centimeters.