4. (6 marks] A bacteria culture initially contains 200 cells. After 1 hour, the bacteria population has grown to 400 cells. Assuming exponential growth, what will be the population after 4 hours? Simplify your answer as much as possible.

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8. At noon, a bacteria culture has 4,000 bacteria. At 1 p.m., the bacteria population has grown to 4,400. Assuming exponential growth, what will be the bacteria population at 3 p.m.? @ 5,000 ® 5,200 © 5,432 © 5,284 © 5,324

A culture of the bacteria E. coli is grown in a petri dish. The initial sample had 5 E. coli bacteria when the experiment began. E. coli is a bacteria that grows very quickly, doubling its population every 15 minutes under ideal conditions. The experiment is left to run overnight for 8 hours and then for the rest of the day (24 hours total).

a. Express the population of E. coli,

, as an exponential function of the time elapsed since the experiment began.

b. What was the total amount of E. coli after 8 hours?

c. After 24 hours, the amount of E. coli was estimated by mass to be

. Is that what was expected from our exponential growth model?

6. A small lake is stocked with a certain species of fish. Use the simplified logistic model 4 P(t) = 1 to describe the population at time t > 0. The parameters A and k are positive constants. (b) After 4 years the population is 1500. What will the population be after 8 years? (Note that using the properties of the exponential function, you are expected to obtain an exact numerical answer, with no unevaluated exponentials or logarithms.)

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4. (6 marks] A bacteria culture initially contains 200 cells. After 1 hour, the bacteria population has grown to 400 cells. Assuming exponential growth, what will be the population after 4 hours? Simplify your answer as much as possible.

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