Modeling Bacteria Growth Using Exponential Function

TLDR; Bacteria growth is modeled using the continuous exponential function, with the population determined after 30 days at a 16% growth rate.

💡 Bacteria Growth Model

The initial scenario involves 1,000 bacteria growing continuously at a rate of 16% per day.

To model the number of bacteria and determine the population after a specific time, a function is needed.

The continuous exponential growth function is used due to the continuous growth rate.

The function P(T) = P0 x e^(kt) is applied, where P(T) represents the population after time T, P0 is the initial amount, k is the growth rate, expressed as a decimal, and t is the time.

🔄 Using the Exponential Growth Function

From the given information, the function P(T) = 1,000 x e^(0.16t) is derived, where the continuous growth rate of 16% is expressed as a decimal (0.16).

The exponent in the function is determined as 0.16 x t, where t is the time in days.

P(T) represents the number of bacteria after T days.

📈 Determining Bacteria After 30 Days

To find the number of bacteria present after 30 days, P(30) is calculated using the function 1,000 x e^(0.16*30).

Using a calculator, the exponential expression is evaluated to approximately 121,510, indicating the number of bacteria after 30 days.