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A bacteria culture initially contains 200 cells and grows at a rate proportional to its size. After 4 hours the population has increased to 270. (a) Find an expression for the number of bacteria after t hours. P(t) = (b) Find the number of bacteria after 8 hours. (c) Find the rate of growth after 8 hours. (d) When will the population reach 9000?The half-life of cesium-137 is 30 years. Suppose we have a 800-mg sample. a) Find the mass that remains after t years. m(t) = b) How much of the sample remains after 160 years? c) After how long will only 6 mg remain?A roast turkey is taken from an oven when its temperature has reached 170 Fahrenheit and is placed on a table in a room where the temperature is 70 Fahrenheit. (a) If the temperature of the turkey is 150 Fahrenheit after half an hour, what is its temperature after 45 minutes? Fahrenheit. (b) When will the trukey have cooled to 95 Fahrenheit? hours. If 3000 dollars is invested at 8% interest, find the value of the investment at the end of 8 years if interest is compounded a) annually b) quarterly c) monthly d) continuously