Question

If there are 8520 bacteria present after 15minutes find K and round to the nearest thousandth (picture below)

Answer 1

Choice A

Explanation:

The scenario presented relates to exponential growth models; the population of bacteria is growing at an exponential rate given by the equation;

`B=1000e^(kt)`

In this case B represents the population of the bacteria, t the time in minutes, k the growth constant and 1000 represents the initial population at time 0.

After 15 minutes, the population of bacteria grows to 8520. This implies that B is 8520 while t is 15. We substitute this values into the given equation and solve for k, the growth constant;

`8520=1000e^(15k)`

Divide both sides by 1000;

`8.52=e^(15k)`

The next step is to introduce natural logs on both sides of the equation;

`ln8.52=ln(e^(15k))\\ln8.52=15k\\k=(ln8.52)/(15)=0.143`