Question

A scientist is growing bacteria, starting with a culture of 10 bacteria. The colony of bacteria doubles every 3 hours. Which equation represents the relationship between the number of bacteria (b) and the number of hours (t) that have elapsed?

A) B= 10(2)^t
B) B= 10(2)^t/3
C) B= 10(2)^3t
D) B= 10(e)^2t
E) B= log₂(t)

Answer 1

• Initial amount of bacteria=10
• Doubles in every 3 hours
• Means time is t/3

So

The expression is

`\\ \rm\rightarrowtail B=10(2)^{(t)/(3)}`

Option B is correct

Answer 2

B) B=10(2)^(t/3)

Explanation:

The Formula used to find Exponential Growth is

`y=a*b^{(t)/(t_(1) ) }`

where y is the Final Amount

a is the Initial Amount

b is the Growth Factor

t is Time

t1 is Time to Complete one Growth

so for our Problem

a=10 and b=2 and t1=3 and y=B

so B=10(2)^(t/3)