Solve the problem. 27) The size of an insect colony t days after its formation is P( t) 1000e0.2t, Approximately how many insects are present after 10 days? 28) How much money has to be invested now at 8% continuous interest in order to have $1000 after 5 years? 29) A high-yield savings pays 8% interest, compounded continuously. How long would it take an initial investment of $2500 to grow to $12,500 30) A bacterial culture grows exponentially; that is, P)-100ekt, where P(t) is the size of the culture at time t hours. Suppose that after 2 hours the size of the culture is 400. What is k (approximately)? 31) If a population has a growth rate of 6% per year, howlong to the nearest tenth of a year will it take the population to double? 32) Plutonium has a decay rate of 0.003% per year, what is the half life? 33) An object's acceleration at time t is given by v(0)-14t, and its initial velocity v(O) is 35 Find the velocity function v(t) 34) An object moves in such a way that its velocity (in meters per second) after time t (in seconds) is given by v 2+6+3 Find the distance traveled by the object during the first four seconds.
Show transcribed image text Solve the problem. 27) The size of an insect colony t days after its formation is P( t) 1000e0.2t, Approximately how many insects are present after 10 days? 28) How much money has to be invested now at 8% continuous interest in order to have $1000 after 5 years? 29) A high-yield savings pays 8% interest, compounded continuously. How long would it take an initial investment of $2500 to grow to $12,500 30) A bacterial culture grows exponentially; that is, P)-100ekt, where P(t) is the size of the culture at time t hours. Suppose that after 2 hours the size of the culture is 400. What is k (approximately)? 31) If a population has a growth rate of 6% per year, howlong to the nearest tenth of a year will it take the population to double? 32) Plutonium has a decay rate of 0.003% per year, what is the half life? 33) An object's acceleration at time t is given by v(0)-14t, and its initial velocity v(O) is 35 Find the velocity function v(t) 34) An object moves in such a way that its velocity (in meters per second) after time t (in seconds) is given by v 2+6+3 Find the distance traveled by the object during the first four seconds.