A population of bacteria doubles every 15 hours. Initially, the population of bacteria is 40. What is the population of the bacteria after 40 hours? Round to the nearest whole number.I would really appreciate any kind of help. PLEASE HELP ME ASAP!
Accepted Solution
A:
Answer:The population of the bacteria after 40 hours is 254.Step-by-step explanation:The initial population is 40 and the population of bacteria doubles every 15 hours.The population function is defined as[tex]P(t)=P_0\cdot (b)^{t}[/tex]Where P₀ is initial population, b is exponential growth rate.Since the population of bacteria doubles every 15 hours, therefore the growth rate is[tex]2^{\frac{1}{15}}[/tex][tex]P(t)=40\cdot (2)^{\frac{1}{15}t}[/tex][tex]P(t)=40\cdot (2)^{\frac{t}{15}}[/tex]We have to find the population of the bacteria after 40 hours, so put [tex]t=40[/tex] in the above equation.[tex]P(t)=40\cdot (2)^{\frac{40}{15}}[/tex][tex]P(t)=40\times 6.3496[/tex][tex]P(t)=253.9842[/tex][tex]P(t)\approx 254[/tex]Therefore the population of the bacteria after 40 hours is 254.