Question

On the planet Rigel 8, there are microorganisms that split into 3 identical copies every second,
and never die.
1. What function describes the growth of a population of these microorganisms as a function oftime, if at time 0 there is just one lone microorganism?

Answer 1

2. What is the doubling time for the function 3t?
3. Write down the condition for a function to have a doubling time.
4. Express the function 3t in terms of the base 2 exponential. Where does the doubling time
appear? Can you interpret this as a change of units for measurement of time?
5. Suppose f has a doubling time h and f(0) = 1. How can you express h in terms of f−1?
What does this say when f is the exponential to the base a (a > 0, a 6= 1)?

Answer 2

actually this i think i have this one worked out if i think for a while hmm