Population are often represented using exponential functions
The population of the bacteria on day 30 is 134837
Let x represent the number of days, and y represents the population.
So, we have: (x,y) = (1,8500), (2, 9350) (3, 10285)
An exponential functions is represented as [tex]\mathbf{y = ab^x}[/tex]
So, we have:
[tex]\mathbf{8500 = ab}[/tex]
[tex]\mathbf{9350 = ab^2}[/tex]
Divide both equations
[tex]\mathbf{\frac{9350}{8500} = \frac{ab^2}{ab}}[/tex]
[tex]\mathbf{1.1 = b}[/tex]
Rewrite as:
[tex]\mathbf{b = 1.1 }[/tex]
Substitute 1.1 for b in [tex]\mathbf{8500 = ab}[/tex]
[tex]\mathbf{ 8500 = 1.1a}[/tex]
Divide both sides by 1.1
[tex]\mathbf{ 7727.3 = a}[/tex]
Rewrite as:
[tex]\mathbf{ a = 7727.3 }[/tex]
So, we have:
[tex]\mathbf{y = ab^x}[/tex]
[tex]\mathbf{y = 7727.3 \times 1.1^x}[/tex]
On day 30, we have: x = 30.
So, the equation becomes
[tex]\mathbf{y = 7727.3 \times 1.1^{30}}[/tex]
[tex]\mathbf{y = 134837}[/tex]
Hence, the population of the bacteria on day 30 is 134837
Read more about exponential functions at:
https://brainly.com/question/11487261
