The equation is, [tex]\rm y = 30(1+0.50)^x[/tex] 101.25 bacteria cells after 3 hours, and 3892 bacteria cells after 12 hours will be present,
It is given that the sample of bacteria cells in a petri dish increases by 50% every hour, a scientist starts with a sample of 30 bacteria cells.
It is required to find the equation that can be used to determine the number of cells after x hours.
What is Exponential Growth?
It is defined as increasing an amount by a definite percentage over the span of a time, the original amount increases exponentially.
We know the Exponential Growth equation written as:
[tex]\rm y= a(1+r)^t[/tex]
Where y = total amount,
a = starting amount
r = the growth rate/exponential decay rate as a decimal
t = number of growth periods.
We have a = 30
r = 50% = 0.50
t = x
Putting these values in the Exponential Growth equation, we get:
[tex]\rm y = 30(1+0.50)^x[/tex] this is the equation for Exponential Growth.
If x = 3 hours, then:
[tex]\rm y = 30(1+0.50)^3 \Rightarrow 30(1.50)^3\Rightarrow 30(3.375)\Rightarrow 101.25\\[/tex]
If x = 12 hours, then:
[tex]\rm y = 30(1+0.50)^1^2 \Rightarrow 30(1.50)^1^2\Rightarrow 30(129.746)\Rightarrow 3892.39\approx 3892[/tex]
Thus, the equation that can be used to determine the number of cells after x hours is, [tex]\rm y = 30(1+0.50)^x[/tex], that 101.25 bacteria cells will be present in the dish after 3 hours, and 3892 bacteria cells will be present after 12 hours.
Learn more about Exponential Decay here:
brainly.com/question/2193820
