Question

bacteria are growing in culture and the number is incre asing at the rate of 5% an are initially 400bacteria are present determine an equation that gives the number and of bacteria present after t hours

Answer 1

The equation to represent the exponential growth of bacteria in this context is N(t) = 400 × (1.05)^t, where N(t) is the number of bacteria after t hours, the growth rate is 5%, and the initial quantity of bacteria is 400.

Step-by-step explanation:

The student is asking for an equation that represents the exponential growth of a bacterial culture with a constant growth rate. In this scenario, the growth rate is 5% per hour and the initial number of bacteria is 400. Since bacteria grow exponentially, the equation to determine the number of bacteria after t hours can be represented using the formula for exponential growth:

N(t) = N_0 × (1 + r)^t

Where N(t) is the number of bacteria after t hours, N_0 is the initial number of bacteria, r is the growth rate as a decimal, and t is the time in hours. To find the equation:

1. Convert the growth rate from a percentage to a decimal by dividing by 100: 5% / 100 = 0.05.
2. Plug in the values: N_0 = 400 and r = 0.05 into the formula.
3. The resulting equation will be: N(t) = 400 × (1 + 0.05)^t.

So, the equation that gives the number of bacteria present after t hours when bacteria are growing in culture and the number is increasing at a rate of 5% an hour with initially 400 bacteria present is: N(t) = 400 × (1.05)^t.