1. ## Differential equation

1. Gainsville had a population of 25000 in 1970 and a population of 30,000 in 1980. Assume that its population will continue to grow exponentially at a constant rate. What population can the Gainsville city planners expect in the year 2010?

2. Suppose that \$1000 is deposited in a savings account that pays 8% annual interest compounded continuously, At what rate (in dollars per year) is it earning interest after 5 year? After 20 year?

3. In a certain culture of bacteria , the number of bacteria increased sixfold in 10h. Assume natural growth, how long did it take for their number to double?

4. Let f(x)= 3x + 4, x(y)= y-9, and y(z)= z^2 + 1. Implicitly, if z=3, what does f equal to?

5. The salt KNO3 dissolves in methanol at a rate x'(t)= (0.8)x -(0.004)x, where x is the number of grams of salt in solution after t seconds. Let x(0)= 50 . What x is the value of t such that x(t)= 100 (report to the nearest hundredth of a second)?

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