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11. A population of bacteria grows according to an exponential model. The initial size of the population is P, and 45 minutes later the population has grown to a size of 3P.. (a) Give an equation for the size P(t) of the population, after t seconds. Find all parameters involved.

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Sixta Kovacek
Sixta KovacekLv2
2 Dec 2018
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2. There are 30 guinea pigs introduced into an ecosystem, and their population grows at a rate proportional to its size. In 2 years, the population grows to 85 guinea pigs. (a) Find a formula for the function P(t) that gives the population of guinea pigs at any time t measured in years. [5] [4] (b) Using your answer to part (a), determine how long it would take the guinea pig population to quadruple.

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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