Section 6.6: Growth and Decay Model Theorem 6.33: If y is a differentiable function of t such that y > 0 and, for some constant c, then where y 0 is the.

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Section 6.6: Growth and Decay Model Theorem 6.33: If y is a differentiable function of t such that y > 0 and, for some constant c, then where y 0 is the value of y at t = 0. y 0 is the initial value of y, and c is the proportionality constant. Exponential growth occurs when c > 0, and exponential decay occurs when c < 0.

Example 1 When t = 0, y = 5, and when t = 3, y = 10. Given that the rate of change of y with respect to t is directly proportional y, find the value of y when t = 6.

Example 2 Bacteria increase from 600 to 1800 in 2 hours. If the rate of increase is directly proportional to the number of bacteria, write a formula that will allow you to calculate the number of bacteria at the end of four hours, then five hours.

Example 3 Radium decays exponentially and has a half life of 1600 years. Find a formula for the amount remaining after t years if you start with 50 mg. When will there be exactly 20 mg left?