Question

Hank is studying a population of bacteria and notices that the bacteria population decreases by 5% each hour. The function that represents the population of bacteria has a constant percent rate of change.

Answer 1

Answer: Pupulation = A*0.95^t

where t is the numer of hours that has passed, and A is the initial population of the bacteria.

Explanation:

If the initial population of bacteria is A.

After one hour we can see that the population has decreaesed by 5%, so the new population is

P = A - 0.5*A = 0.95*A

After other our, the population decreased by 5% again, the new population is:

P = (0.95*A) - 0.5*(0.95*A) = 0.95*0.95*A = A*0.95^2

And so on.

This is an exponential decay, so we can write this relation as:

Pupulation = A*0.95^t

where t is the numer of hours that has passed, and A is the initial population of the bacteria.