Help me with these 2 problems
1. It is known that Carbon-14 atoms decay in an exponential manner. It takes about 5730 years for Carbon-14 atoms to decay to half their original amount. How many years will it take for the Carbon-14 atoms inside an object to decay to one-eighth of their original amount?
2. In a colony of bacteria, the rate at which the number of bacteria grows increases linearly with time (i.e. the number of new bacteria produced per unit time increases proportionally with time). Initially at time t = 0 hour there are 5 million bacteria in the colony and the initial rate of bacteria produced is 1 million per hour. At time t = 5 hours, the growth rate of the bacteria has increased to 6 million bacteria per hour.
a. What is the growth rate of bacteria at t = 2 hours?
b. What is the total number of bacteria at time t = 5 hours?
c. What is the average number of bacteria produced every hour during this 5 hours interval?
Perhaps these qns may seem basic, but i dont know why i just couldnt get the answers. Pls help me.