Answer:
the first one is "exponential"
then "12"
the last one is "multiply 1.5"
The relationship between the time, in hours, and the population of the bacteria is exponential the y-intercept of the function is 12 and the rate of change of the function is 1.5.
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
For this case we have a function of the form:
y = A x b²
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 x b¹
After 2 hours, the population is 27:
27 = A x b²
We have a system of two equations with two unknowns dividing equations we have:
[tex]\dfrac{ A \times b^2}{ A \times b^1} = \dfrac{ 27}{ 18}[/tex]
b = 27 / 18
b = 1.5
Substituting b in equation 1 we have:
18 = A x ( 1.5 )
A = 18 / 1.5
The function is:
y = 12 x (1.5 )[tex].^x[/tex]
Therefore, the relationship between the time, in hours, and the population of the bacteria is exponential the y-intercept of the function is 12 and the rate of change of the function is 1.5.
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