Exponential Growth and Decay Exponential Growth: If an initial amount /, is increasing at a rate of % per time period, then the amount after / time periods can be modeled by: n(1) = no (1+r)' Exponential Decay: If an initial amount ll, is decreasing at a rate of % per time period, then the amount after / time periods can be modeled by: n(1) = no(1-r)' Continuous Growth: If an initial amount /, is increasing at a rate proportional to its size, where r is the relative growth rate, then the amount after I time periods can be modeled by: n(t ) = me" Continuous Decay: If an initial amount /, is decreasing at a rate proportional to its size, where r is the relative decay rate, then the amount after / time periods can be modeled by: n (1 ) = ne" Exponential Applications Practice 1. A certain culture of the bacterium initially has 10 bacteria and is observed to double every 1.3 hours. Determine a model /1(1) for the number of bacteria in the culture after , hours. b. Estimate the number of bacteria present after 35 hours. c. When will the bacteria count reach 10,000? 2. A certain species of rabbit was introduced to France 40 years ago. Biologists observed that the population doubles every 8 years, and now the population is 9,600. a. What was the initial size of the rabbit population? b. Estimate the size of the rabbit population 5 years from now. 1703. A grey squirrel population was introduced onto a small island about 4 months ago. The current grey squirrel population on the island is estimated to be about 200 and doubling every 4 months. a. What was the initial size of the squirrel population? b. Estimate the squirrel population 1 year after they were introduced onto the island, 4. The half-life of Cs137 is 30.2 years. Suppose we have a sample with amass of 1 kg. a. Write a function llilll that models the mass remaining-.3 after I years. b, How much Cs137 will remain after 151 years? 5. The halfilife of radium-226 is 1600 years. Suppose we have a 25 mg sample. a. Write a function \"1(1) that models the mass remaining after I years. b. How much of the sample will remain after 3000 years? c. After how long will only 15 mg of the sample remain? 6. The halflife of strontium90 is 28 years. How long will it take a 30 mg sample to decay to 20 mg? 7. A 64 g sample of Germanium-66 is left undisturbed for 12.5 hours. At the end of that period. only 2.0 g remain. What is the half-life of this material? 8. Radon has a half-life of 3.8 days. After 7.6 days, 6.5 g remain. What was the mass of the original sample