MATH SOLVE

3 months ago

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

Accepted Solution

A:

Answer:Choice AStep-by-step explanation:The scenario presented relates to exponential growth models; the population of bacteria is growing at an exponential rate given by the equation;[tex]B=1000e^{kt}[/tex]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;[tex]8520=1000e^{15k}[/tex]Divide both sides by 1000;[tex]8.52=e^{15k}[/tex]The next step is to introduce natural logs on both sides of the equation;[tex]ln8.52=ln(e^{15k})\\ln8.52=15k\\k=\frac{ln8.52}{15}=0.143[/tex]