SOLUTION: The Greek God Zeus ordered his blacksmith Hephaestus to create a perpetual water-making machine to fill Zeus' mighty chalice. The volume of Zeus' chalice was reported to hold about

Question 469372: The Greek God Zeus ordered his blacksmith Hephaestus to create a perpetual water-making machine to fill Zeus' mighty chalice. The volume of Zeus' chalice was reported to hold about one hundred and fifty sextillion gallons (that is a fifteen followed by twenty-two zeros). If Hephaetus' machine pours out 2 gallon in the first minute and then doubles its output each minute, find in which minute would this hypothetical machine pour out a single quantity of water that would be enough to fill Zeus' chalice with water?

The "learning curve" describes the rate at which a person learns certain tasks. If a person sets a goal of typing N words per minute (wpm), the length of time t (in days) to achieve this goal is given by the following formula.
t = - 62.5 ln$1-N/80$
(a) According to this formula, what is the maximum number of words per minute?

(b) Solve for N.
N =

The atmospheric pressure P in pounds per square inch (psi) is given by the formula below, where a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 13.25 psi, what is its altitude? (Recall that 1 mi = 5,280 ft. Round your answer to the nearest foot.)
P = 14.7 e**(-0.21 a)
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
We want the least positive integer such that

taking common logs of both sides, we get

<==>
==> let x = 77. Hence after the 77th minute.
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