Question

Please help me!

Answer 1

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:

$f(x)=10*2^{\frac{x}{3} }$

Given the bacteria on the stove is measured at 10 and doubles every 4 days we can create another equation:

$f(x)=10*2^{\frac{x}{4} }$

To find how many days it will take for the bacteria population to equal the same lets set both equations equal to eachother:

$10*2^{x/3}=10*2^{x/4}$

Divide both sides by 10

$2^{x/3}=2^{x/4}$

Since both exponents have the same base we can set the exponents equal to eachother and solve for x:

$\frac{x}{3}=\frac{x}{4}$

Multiply both sides by 3 to isolate x on the left side

$x=\frac{3x}{4}$

Multiply both sides by 4 to remove fraction

$4x=3x$

Subtract 3x to isolate x on the left side

$x=0$

Plug x into one of our original equations

$f(0)=10*2^{0/3}$

Solve

$f(0)=10$