Answer:
They are only equal on day 0, both having 10 population.
Step-by-step explanation:
Given the bacteria on the counter is initially measured at 5 and doubles every 3 days we can generate the following geometric equation:
[tex]f(x)=10*2^{\frac{x}{3} }[/tex]
Given the bacteria on the stove is measured at 10 and doubles every 4 days we can create another equation:
[tex]f(x)=10*2^{\frac{x}{4} }[/tex]
To find how many days it will take for the bacteria population to equal the same lets set both equations equal to eachother:
[tex]10*2^{x/3}=10*2^{x/4}[/tex]
Divide both sides by 10
[tex]2^{x/3}=2^{x/4}[/tex]
Since both exponents have the same base we can set the exponents equal to eachother and solve for x:
[tex]\frac{x}{3}=\frac{x}{4}[/tex]
Multiply both sides by 3 to isolate x on the left side
[tex]x=\frac{3x}{4}[/tex]
Multiply both sides by 4 to remove fraction
[tex]4x=3x[/tex]
Subtract 3x to isolate x on the left side
[tex]x=0[/tex]
Plug x into one of our original equations
[tex]f(0)=10*2^{0/3}[/tex]
Solve
[tex]f(0)=10[/tex]
