Logarithmic function help

1. How long would it take for $25 to increase to $500 at 7.6% compounded annually? Round off your answer to the nearest year.

2. The population of a colony of bacteria doubles every 3 hours. How long, in hours, does it take for the population to be 3.5 times its original size? Answer correct to one decimal place.

3. Suppose the exponential model of a population growth is given by

P(t) = P010kt,

where P0 equals the original or initial population and t is time in hours. Find k, if a population of a culture is 540 now and is 2200 in 11 hours. (Accurate to 3 decimal places)

4. 210 grams of a radioactive substance decays to 80 grams after 880 years. To the nearest year, what is the half-life of the substance?

5. Earthquake intensity is given by I = Io(10)m, where Io is the reference intensity and m is magnitude. A particular major earthquake of magnitude 7.4 is 70 times as intense as a particular minor earthquake. The magnitude, to the nearest tenth, of the minor earthquake is

Logarithmic Applications Formula.

A = AO (B)^ T/P

A= Future Amount

Ao = Intial Amount

B = Type of growth

P = Period for Growth to occcur

T = Elaspsed Time.