Helpp exponent & logarithmic problems!!

sirs Sorry for this long questions in my post because its already our finals and i cant seem to answer our reviewer with so many undiscussed LOg problems!!! i wont do this again....

U can answer as many...

Exponential growth / decay

2.) In year 2000, it was expected that for the succeeding 20 years the population of a particular town would be y people t years from 2000, where y = C10 ^ (kt) and C and k are constants. If the actual population in 2000 was 10,000 and in 2005 it was 40,000 what is the expected population in 2015?

3.) Suppose the amount of oil pumped from one of the oils wells in jeddah decreases at the continuous rate of 10% per year. When will the well's output fall to one-fifth of its present value? use the typical equation growth decay.

Heat transfer: Newton's Law of Cooling

4) Soup Left in a tin cup cools to the temperature of the surrounding air. a hot silver ingot immersed in water cools to the temperature of the surrounding water. In situations like these, the temperature of a hot object changes w/ time according to the newton's law of cooling:

T - Ts = ( To - Ts) e ^ -kt

where T is the temperature of the hot object at time t, Ts is the surrounding temperature that is assumed constant, To is the value of T at time zero and k is called the heat transfer coefficient, also a constant. The equation is also applicable to the case of a warming object.

Now suppose a hard - boiled egg at 98 degrees Celsius water to cool. After 5 minutes, the egg's temperature is found to be 38 degrees Celsius. Assuming that the water has not warmed appreciably, how much longer will it take the egg to reach 20 degrees celsius?

Electric Circuits

6.) A simple electric circuit containing no condensers, a resistance of R ohms, and an inductance of L henries has the electromotive force cut off when the current is Io amperes. The current dies down so that at t seconds the current is i amperes, and i = Io e^ -(R/L)t. Use natural logarithms to solve this equation for t in terms of i and the constants R, L and Io.