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A biologist places a colony consisting of 5000 bacteria into a petri dish. After the intial placement of the bacteria at time t = 0, the biologist measures and estimates the number of bacteria present every halfhour. This data was then fitted by an exponential curve of the form y=c.2^(kt) where c and k are constants, t is measured in hours, and y is measured in thousands of bacteria. The scatterplot together with the exponential curve are shown below. Suppose that the data was fitted with a quadratic function of the form t^(2)+bt+c instead of an exponential function. Assume that the quadratic funtion agrees with the scatterplot at times t = 0 and t = 6. What is the t - coordinate of the vertex of the graph of the quadratic function? |
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