The number of bacteria in a culture is increasing according

The number of bacteria in a culture is increasing according to the law of exponential growth. The initial population is 500 bacteria, and after 10 hours there are 1500 bacteria. a. Write down an exponential growth model to represent P(t), population as a function of time. b. Determine the population after 24 hours. Also find how long until the population reaches one million (1,000,000). c. If the population continues to grow at this rate, what issue can you observe relating to increasing numbers of bacteria with increasing time?

Solution

The exponential growth model is

y= a e^kt

In the given question a=500

y= 1500

and t=10

1500=500e^10k

e^10k=3

k= ln3/10

a. Growth model is

P(t)=500 e^{t ln3/10}

b. t=24

p(24)=500e^24ln3/10=500 * 3^24/10= 6983.3

1000000=500 e^{t ln3/10}

2000= 3^.t

10log 2000/log3=t

t=69.18 hrs