Question

The number of bacteria in a culture is modeled by the function n(t)=500e⁰.⁴⁵t where t is measured in hours a) What is the initial number of bacteria?

Answer 1

The initial number of bacteria in the given culture is 500, which is determined by substituting t with 0 in the given function n(t) = 500e^0.45t.

Step-by-step explanation:

The initial number of bacteria in a culture can be found by evaluating the function n(t) = 500e0.45t when time t is 0. When t equals 0, the exponential part of the function e0.45t simply becomes 1 because any number raised to the 0 power is 1.

Therefore, the initial number of bacteria, n(0), is 500e0 = 500. This is because the only thing remaining from the function is the coefficient 500, as e0 equals 1.