A strain of E-coli Beu 397-recA441 is placed into a nutrient broth at 30° Celsius and allowed to grow. The following data are collected. Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth. The population is measured using an optical device in which the amount of light that passes through the petri dish is measured.

Time (hours), x            Population, y

0 ………………………... 0.09

2.5…………………….…. 0.18

3.5 ……………………..... 0.26

4.5 ………………………. 0.35

6 ……………………..….. 0.50

(a) Draw a scatter diagram treating time as the independent variable.

(b) Using a graphing utility, build an exponential model from the data.

(c) Express the function found in part (b) in the form N (t) = N₀e^kt.

(d) Graph the exponential function found in part (b) or (c) on the scatter diagram.

(e) Use the exponential function from part (b) or (c) to predict the population at x = 7 hours.

(f) Use the exponential function from part (b) or (c) to predict when the population will reach 0.75.