Question

Scientists studying a bacteria sample find that after starting with 120 cells, the number of cells doubles every hour.

Which of the following equations is a function that will predict C(h), the number of cells after h hours have passed?

Answer 1

Step-by-step explanation:

Given:-

Scientists studying a bacteria sample find that after starting with 120 cells, the number of cells doubles every hour.

To find:-

Which of the following equations is a function that will predict C(h), the number of cells after h hours have passed?

Solution:-

Given that

The starting number of cells in the sample bacteria = 120

After one hour , The number of cells doubles = 2×120 = 240

After one hour the number of cells = 2×240 = 480

We get the list of number of cells in the sample bacteria are 120,240,480,...

First term (a)= 120

second term = 240

Common ratio (r)

= 240/120 = 2

=480/240=2

Since the common ratio is same throughout the series

They are in the GP

we know that

The General or nth term of the GP

tn = a×r^(n-1)

the number of cells after h hours have passed

t h = 120×(2)^(h-1)

=> t h = 120×2^h /2^1

Since a^m/a^n = a^(m-n)

=> t h = (120/2)× 2^h

=> t h = 60×2^h

Answer:-

The number of cells after h hours have passed

is 120×2^(h-1) or 60×2^h

Used formulae:-

• The General or nth term of the GP
• tn = a×r^(n-1)
• a = first term
• r = Common ratio
• n = number of terms