1. The number of bacteria in a culture begins with approximately 10,000 organisms at the start of an experiment. If the bacteria doubles every 5 hours, the model P(t) = 10000(2):/5 represents the population P(t) after t hours. %3| a. Write a function of the form P(t) = Poekt to model the population. %3D

If 00 = 4, 01 = 2.5, plot the graph of ho(x) = 00+ 01x. %3D %3D

The table shows a city's population at 10-year intervals from 1970 to 2000. t = 0 represents 1970. %3D t: years since 1970 10 20 30 P: population 240 710 2130 6450 al Use exponential regression and all the data points to write an equation for the function, P = f (t) for the population, t years after 1970. Round your "a" and “b" values in your equation to 4 decimal places. b) Using your regression equation, determine the predicted population in 2025 (to the nearest person).

The biologist has a second culture to examine. She knows that the population of the culture doubles every 15 minutes. After 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. 2. (a) What was the size of the initial population? Predict the size of the culture at t=3 hours. What was the size of the population at 40 minutes? Explain and justify your answers. (b) Create a graph of the population as a function of time. Find an equation that can be used to predict the size of the population at any time t. (c) Examine the rate at which the bacteria culture is growing. How fast growing after 1 hour? After 1.5 hours? After 2 hours? Use a time interval of h = 0.01 hours to estimate these rates. Interpret these rates in terms of the context of the problem situation. How do these three rates compare? (d) the culture