Question

Each bacterium in a petri dish splits into 2 bacteria after one day. The function b(d) = 600 • 24 models

the number of bacteria, b, in the petri dish after d days.

Part A)

What is the initial number of bacteria in the petri dish?

Part B)

How many bacteria will be in the petri dish after 5 days?

Answer 1

(a)Initial Number of Bacteria=600

(b)
`\text{Number of bacteria after 5 days}=19200`

Explanation:

Given an initial number
`b_0` of bacteria in a petri dish, and each bacteria splits into 2 bacteria after one day.

The function
`b(d) = 600 \cdot 2^d` models the number of bacteria, b after d days.

Part A

Given
`b(d) = 600 \cdot 2^d`

When d=0,

The initial number of bacteria in the petri dish,

`b_0=b(0) = 600 \cdot 2^0=600`

Part B

After 5 days, when d=5

`b(5) = 600 \cdot 2^5=600 \cdot 32\\\text{Number of bacteria after 5 days}=19200`