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# A student is trying to determine the half-life of radioactive iodine-131. He measures the amount, , of iodine-131 in a sample solution every 8 hours....

A student is trying to determine the half-life of radioactive iodine-131. He measures the amount, , of iodine-131 in a sample solution every 8 hours. His data are shown in the table. Time (h) 0 8 16 24 32 40 48 Amount (g) 8.64 8.32 8.18 7.82 7.7 7.42 7.22 (a) Find an appropriate exponential model of the data points. Amount at time , . (b) Find the half-life of idoine-131 according to the exponential model in part (a). Half-life, . Solve if the solution passes through the point . Graph the solution. help (formulas) The total number of people infected with a virus often grows like a logistic curve. Suppose that 25 people originally have the virus, and that in the early stages of the virus (with time, , measured in weeks), the number of people infected is increasing exponentially with . It is estimated that, in the long run, approximately 4500 people become infected. (a) Use this information to find a logistic function to model this situation. (b) Sketch a graph of your answer to part (a). Use your graph to estimate the length of time until the rate at which people are becoming infected starts to decrease. What is the vertical coordinate at this point? vertical coordinate =

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Sol: (1) (a)
We use the formula,
…………….. (1),
When
From the equation (1),
On taking a log both sides,
(b) So
We require when We could write our function as
Sol: (2)
On taking an...

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