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Two boats leave the shore at the same time to take supplies to neighboring islands. One of the boats returns every 45 minutes. The other boat returns every hour. How long will it take for the two boats to return at the same time?

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[4] 7. (a) A function f is said to grow exponentially when f'(x) = kf() for some non-zero constant k and all x in R. If f grows exponentially, prove that the function g(t) = is a constant function. [1] (b) If (b) If f grows exponentially, use part (a) to show that f(x) = Aek for some constant A. [5] (c) The population in a dish of bacteria is growing exponentially. At the start there are 8 micro- units of bacteria in the dish and the population doubles every 3 hours. How long will it take for the population to reach 20 micro-units?

 

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