Question

Bt= 8500 *(8/27)^t/3After a special medicine is introduced into a Petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly.

Answer 1

Every 1.71 seconds, the bacteria loses

Explanation:

Given

Required [Missing from the question]

Every __ seconds, the bacteria loses

First, we model the function from t/3 to t.

Apply law of indices

Evaluate each exponent

--- This gives the number of bacteria at time t

At time 0, we have:

Let r be the time 1/2 disappears.

When 1/2 disappears, we have:

So, we have:

Substitute r for t

Substitute

Divide both sides by 8500

Take log of both sides

Apply law of logarithm

Make r the subject

Hence, it reduces by 1/2 after every 1.71 seconds

Answer 2

Every second, the number of bacteria is multiplied by a factor of 0.67

Explanation:

Let's rewrite the base so that the exponent is just t.

(8/27)^t/3=((8/27)^1/3)t=(2/3)^t

Therefore, we can rewrite the modeling function as follows.

B(t)=8500⋅(2/3)t

According to this model, the number of bacteria is multiplied by 2/3 every second. Rounding this to two decimal places, we get 2/3 ≈0.67