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 population loses 1/4 of its size every 44 seconds. The number of remaining bacteria can be modeled by a function, N, which depends on the amount of time, t (in seconds). Before the medicine was introduced, there were 11,880 bacteria in the Petri dish. Write a function that models the number of remaining bacteria t seconds since the medicine was introduced.

Answer 1

`N(t)=11,880((3)/(4) )^{(t)/(44)}`

Explanation:

we know that

The equation of a exponential decay function is given by

`N(t)=a(1-r)^t`

where

N(t) is the number of remaining bacteria

t is the time in seconds every 44 seconds

a is the initial value

r is the rate of change

we have

`a=11,880\ bacteria\\r=1/4`

substitute

`N(t)=11,880(1-(1)/(4) )^{(t)/(44)}`

`N(t)=11,880((3)/(4) )^{(t)/(44)}`