Apopulation of bacteria is initially 6000. after three hours the population is 3000. if this rate of decay continues, find the exponential function that represents the size of the bacteria population after t hours.

The equation is  at a rate of -23%.

Step-by-step explanation:

Decay can be represented by the equation . We can find the rate at which it decays by using t=3 hours and A=3000. This means in this context.

After substituting, we divided by 6000 to each side to get 0.5 on the left. Now to solve for r, we will take the natural log of both sides and use log rules to isolate r.

We know so we were able to cancel it out and divide both sides by 3.

We solve with a calculator

We change -0.23 into a percent by multiplying by 100 to get -23% as the rate.

The equation is

43

step-by-step explanation: