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TB Calculus Milestone #4 [Week 24] 1. Find f'(x) : f(x) = e'Z'lnx 2. Find f'(x) for each: a. f(x) = log (In x) b. f(x) = In (log x) 3. The number of bacteria in a culture increases from 5,000 to 15,000 in 10 hours. Assuming that the rate of increase is proportional to the number of bacteria present, find a formula for the number of bacteria in the culture at any time t. Estimate the number at the end of 20 hours. When will the number be 50,000? 4. One thousand dollars is deposited in a savings account at 10% interest compounded continuously. (a) Give the formula for Mt), the compound amount after t years. (b) How much will be in the account after 5 years? (c) After 5 years, at what rate will AU) be growing? (d) How many years are required for the balance in the account to reach $3000? 5. Differentiate: y = |n(e" + 3e")