Question

A science 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 3!!!!!!!*** LIMITED TIME!!!!!!

Answer 1

For this case we have a function of the form:
 $y = A * b ^ x$
 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:
 $18 = A * b ^ 1$
 After 2 hours, the population is 27:
 $27 = A * b ^ 2$
 We have a system of two equations with two unknowns
 Dividing equations we have:
 $\frac{A * b ^ 2}{A * b ^ 1} = \frac{27}{18}$
 $b= \frac{27}{18}$
 $b = 1.5$
 Substituting b in equation 1 we have:
 $18 = A * (1.5) ^ 1$
 Clearing A we have:
 $A = 18 / 1.5 A = 12$
 So, the function is:
 $y = 12 * (1.5) ^ x$
 Answer:

 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

Answer 2

Answer:

1. exponential 2. 12 3. multiply 1.5

Step-by-step explanation: