OG详解-OG1 数学1 Q15

Choice D is correct. Let y represent the number of cells per milliliter x hours after the initial observation. Since the number of cells per milliliter doubles every 3 hours, the relationship between x and y can be represented by an exponential equation of the form  y=​a(b)xk，
where a is the number of cells per milliliter during the initial observation and the number of cells per milliliter increases by a factor of b every k hours. It’s given that there were 300,000 cells per milliliter during the initial observation. Therefore, a =300,000. It’s also given that the number of cells per milliliter doubles, or increases by a factor of 2, every 3 hours. Therefore, b=2 and k=3. Substituting 300,000 for a, 2 for b, and 3 for k in the equation y=​a(b)xk​ yields y=300,000​(2)x3​. The number of cells per milliliter there will be 15 hours after the initial observation is the value of y in this equation when x =15. Substituting 15 for x in the equationy=300,000​(2)x3​    yieldsy=300,000(2)15​3​ ，ory=300,000(2)5​ . This is equivalent to  y =300,000 (32), or y =9,600,000. Therefore, 15 hours after the initial observation, there will be 9,600,000 cells per milliliter.