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Practice Problems for 1/28

  1. Let \(h(x)=(x-5)^4+11\). Define functions \(f\) and \(g\) such that \(h=f\circ g\). (You can even try to come up with two different pairs of functions whose composition is \(h\).)
  2. Suppose a population of bacteria grows exponentially. Let \(s(t)\) be the number of cells in the colony after \(t\) days.
    1. What is an appropriate domain for the function \(s\)?
    2. Suppose there are initially 50 cells and the number of cells triples each day. Find a formula for \(s(t)\), then use your formula to determine how many cells are in the colony after 10 days.