Ascience experiment begins with a bacterial population of 12. after 1 hour, the population is 18. after 2 hours, the population is 27. which best describes the relationship between the time, in hours, and the population of the bacteria? a: linear b: quadratic c: exponential what is the y-intercept of the function? a: 6 b: 12 c: 15 d: 18 what is the rate of change of the function? a: add 1.5 b: add 6 c: multiply 1.5 d: multiply 6 ***answer all ! *** limited

For this case we have a function of the form:
 
 Where,
 A: initial population
 b: growth rate
 x: time in hours
 y: population after x hours
 We must find the values of A and b, for this we use the following data:
 After 1 hour, the population is 18:
 
 After 2 hours, the population is 27:
 
 We have a system of two equations with two unknowns
 Dividing equations we have:
 
 
 
 Substituting b in equation 1 we have:
 
 Clearing A we have:
 
 So, the function is:
 
 

 A function that best describes the relationship between the time, in hours, and the population of the bacterium is:
 C: EXPONENTIAL

 the y-intercept of the function:
 B: 12

 the rate of change of the function:
 C: MULTIPLY 1.5

Dwould be the answer