The relative growth rate for a certain type of bacteria population is 85% per hour. A small culture has formed and in just 2 hours the count shows to be 12,500 bacteria in the culture. What is the initial number of bacteria in the culture?
Show work if you can.

Initial populatin: 3652 bacteria

Step-by-step explanation:

The rate is 85% per hour.

Let x be the initial population.

After 1 hour:

x1=x+85%×x=x+0.85x=1.85 x

After another hour:

x2=x1+85%×x1=1.85 x1=1.85² x

But x2=12500.

12500=1.85² x

x=12500/1.85²=3652.3 bacteria

Since you cannot have fractions of a bacteria, the initial population was 3652.

step-by-step :

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204