A bacteria culture starts with 960 bacteria and grows at a rate proportional to its size

A bacteria culture starts with 960 bacteria and grows at a rate proportional to its size. After 2 hours there will be 1920 bacteria. 

(a) Express the population after t hours as a function of t. population: (function of t) 

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(b) What will be the population after 8 hours? 

(c) How long will it take for the population to reach 2530 ? 

Assume the world population will continue to grow exponentially with a growth constant k=0.0132 (corresponding to a doubling time of about 52 years), 

it takes 1 2 acre of land to supply food for one person, and there are 13,500,000 square miles of arable land in in the world. How long will it be before the world reaches the maximum population? Note: There were 6.06 billion people in the year 2000 and 1 square mile is 640 acres. 

Hint: Convert .5 acres of land per person (for food) to the number of square miles needed per person. Use this and the number of arable square miles to get the maximum number of people which could exist on Earth. Proceed as you have in previous problems involving exponential growth

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