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1. A population of protozoa develops with a constant relative growth rate of 0.6685 per member per day. On day zero the population consists of two members. Find the population size after eight days. (Round to the nearest whole number.)
2. A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 65 cells.
3. A bacteria culture initially contains 100 cells and growth at a rate proportional to its size. After an hour the population has increased to 240.
4. The half-life of cesium is 30 years. Suppose we have 140-mg sample. Find the mass that remains after t years.
5. A sample of radioactive substance decayed to 93% to its original amount after a year. (Round your answer to two decimal places.)
6. A roast turkey is taken from an oven when its temperature has reached 185 F and is placed on a table in a room where the temperature is 75 F. (Round your answers to the nearest whole number.)
7. When a cold drink is taken from a refrigerator, its temperature is 5 C. After 25 minutes in a 20 C room its temperature has increased to 10 C. (Round your answers to two decimal places.)
8. A freshly brewed cup of coffee has temperature 95 C in a 20 C room. When its temperature is 73C, it is cooling at a rate of 1 C per minute. When does this occur? (Round your answer to two decimal places.)
9. (a) How long will it take an investment to double in value if the interest rate is 8% compounded continuously? (Round your answer to two decimal places.)
(b) What is the equivalent annual interest rate? (Round your answer to two decimal places.)
10. If $2000 is invested at 4% interest, find the value of the investment at the end of 5 years if the interest is compounded as follows. (Round your answer to the nearest cent.)
11. Use the Laws of Logarithms to combine the expression. ln 3 + 2 ln x + 3 ln(x^2 +3)