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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. According to the scatterplot, the biologist'smeasurements indicate that the number of bacteria present quadrupled in 6 hours, and the exponential curve passes through the corresponding data point at time t = 6. The exponential function also agrees with the initial number of bacteria. Compute ck. |
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