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.
You might consider posting these one at a time and show as much detail as you can.
Your first one uses the compound interest formula:
A = amount of money accumulated after t years, including interest.
r = annual rate of interest (as a decimal)
t = number of years the amount is deposited or borrowed for.
n = number of times the interest is compounded per year