Question

After a special medicine is introduced into a petri dish containing a bacterial culture, the number of bacteria remaining in the dish decreases rapidly. The number of bacteria decays by a factor of \dfrac{1}{15} 15 1 ​ start fraction, 1, divided by, 15, end fraction every 6.76.76, point, 7 minutes, and can be modeled by a function, NNN, which depends on the amount of time, ttt (in minutes). Before the medicine was introduced, there were 90{,}00090,00090, comma, 000 bacteria in the Petri dish. Write a function that models the number of bacteria ttt minutes since the medicine was introduced.

Answer 1

Complete Question

After a special medicine is introduced into a petri dish containing a bacterial culture, the number of bacteria remaining in the dish decreases rapidly. The number of bacteria decays by a factor of 1/15, every 6.76minutes, and can be modeled by a function, N, which depends on the amount of time, t (in minutes). Before the medicine was introduced, there were 90,000 bacteria in the Petri dish. Write a function that models the number of bacteria t minutes since the medicine was introduced.

Answer:

Nt = 90,000 × e^t/15

Step-by-step explanation:

The function that models the number of bacteria t minutes since the medicine was introduced is written as

Nt = No×e^λt

Where:

No = The initial number of the bacteria after time t

Nt = The current number of the bacteria after time t

λ = Decay constant or factor

t = Time in years

From the question,

No = 90,000 bacteria

Nt = The current number of the bacteria after time t

λ = 1/15

t = Time in years

Therefore, our function is written as:

Nt = 90,000×e^1/15 × t

Nt = 90,000 × e^t/15