[-I4 Points] LARCALC11 6.2.056.MI. ASK YOUR TEACHER The number of bacteria in a culture is increasing according to the law of exponential growth. There are 145 bacteria in the culture alter 2 hours and 445 bacteria alter 4 hours. (a) Find the initial population. (Round your answer to the nearest whole number.) bacteria (b) Write an exponential growth model for the bacteria population. Let t represent the time in hours. y= (c) Use the model to determine the number of bacteria aer 8 hours. (Round your answer to the nearest whole number.) bacteria (d) Aer how many hours will the bacteria count be 30,000? (Round your answer to two decimal places.) hr Use the function f and the given real number a to find (f)'(a). (Hint: See Example 5. If an answer does not exist, enter DNE. ) f(x) = x3 +7x-1, a=-9 ( F - 1 ) ' ( - 9 ) = X Need Help? Read It Submit Answer5. [1/4 Points] PREVIOUS ANSWERS LARCALC11 6.2.056.MI. ASK YOUR TEACH ER PRACTICE ANOTHER The number of bacteria in a culture is increasing according to the law of exponential growth. There are 145 bacteria in the culture after 2 hours and 455 bacteria alter 4 hours. (a) Find the initial population. (Round your answer to the nearest whole number.) 46 .f bacteria (b) Write an exponential growth model for the bacteria population. Let 1' represent the time in hours. y=|:]x (c) Use the model to determine the number of bacteria after 8 hours. (Round your answer to the nearest whole number.) 4460 X bacteria (d) After how many hours will the bacteria count be 20,000? (Round your answer to two decimal places.) hr