Question

There are 100 bacteria in a jar. Every day, the number of bacteria increases 25%. In approximately how many days will there be 500 bactria in the jar? Pick the closest answer.

A. 3
B. 12
C. 10
D. 2
E. 7

Answer 1

E. 7

Explanation:

General form of exponential equation:
`y=ab^x`

where
`a` is the initial value,
`b` is the growth/decay rate, and
`x` is time.

Given:

• 
  `a` = 100 bacteria
• 
  `b` = 25% increase = 1.25
• 
  `x` = number of days

⇒
`y=100 \cdot 1.25^x`

If y = 500, then:

`\implies 500=100 \cdot 1.25^x`

`\implies 5=1.25^x`

`\implies \ln5=\ln1.25^x`

`\implies \ln5=x\ln1.25^`

`\implies x=(\ln5)/(\ln1.25)`

`\implies x=7.212567439...`

`\implies x \approx7`