Final answer:
The function b1t=500(1.6)t represents exponential growth, with 500 representing the initial number of bacteria. The growth rate for the second study is 1.6, and the difference of 500 and 800 represents the difference in the initial number of bacteria between the two studies.
Step-by-step explanation:
Exponential Growth
The function b1t=500(1.6)t represents the number of bacteria t hours after Dr. Silas begins her study. To determine whether this is exponential growth or decay, we need to examine the base value of the exponential function, which is 1.6 in this case. Since 1.6 is greater than 1, we can conclude that the function represents exponential growth.
The value 500 in the function represents the initial number of bacteria at the start of the study. It is the starting point of the exponential growth.
The growth rate, r, for the function b2t=800(1.6)t can be determined by comparing it to the base value of 1.6. In this case, the growth rate is also 1.6.
The difference of 500 and 800 between the two studies represents the difference in the initial number of bacteria. In the first study, Dr. Silas starts with 500 bacteria, while in the second study, the starting number is 800.