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

1. exponential 2. 12 3. multiply 1.5

Explanation:

Answer 2

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:

`(A * b ^ 2)/(A * b ^ 1) = (27)/(18)`

`b= (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