Salmonella bacteria are a common cause of food poisoning. A recent study found that the bacteria grow exponentially in rats and double in size every 5 hours.
(a) Suppose a rat initially had 10,000 Salmonella bacteria. Write an equation of the form  y(t) = y₀2^t/k so that y(0) = 10,000 and y(5) = 20,000.
(b) Rewrite the equation from part (a) in the form y(t) = y₀ • ɑ^t.
(c) How long will it take the population of 10,000 bacteria to grow to 40,000?
(d) Use your equation from part (a) or (b) to estimate the size of the population of 10,000 bacteria after 24 hours.