Under optimal conditions, a population of Escherichia coli bacteria will double in 17 minutes. Suppose a culture starts with 20,000 bacteria.

(a) Write a function in the form y = y₀2^t/k giving the number of bacteria after t minutes.

(b) Rewrite the function from part (a) in the form y = y₀a^t.
(c) Rewrite the function from part (a) in the form y = y₀e^kt.
(d) Use the function from part (a) to determine the size after 45 minutes of the culture.
(e) Use the function from part (a) to determine the number of minutes before the culture grows to 200,000 bacteria.