Question

A bacterium in a petri dish multiplies by a factor of 31 every day. On day O,

there is 1 bacterium; on day 1, there are 31 bacteria; on day 2, there are
bacteria; on day 3, there are
bacteria, and so on.
What logarithmic equation can be used to find the number of days it takes for
a colony of 1 bacteria to develop?

Answer 1

Explanation:

Given that,

The bacterial increase a factor of 31 every day ,

Day 0 = 1 bacterium = 31^0

Day 1 = 31 bacterial = 31¹

Day 2 = 31× 31 bacterial = 31²

Day 3 = 31 × 31 × 31 bacterial = 31³

And so on,

Then, nth day will have

Day n = 31ⁿ bacterial

So, when will the bacterial be 1,000,000,000

Then,

31ⁿ = 1,000,000,000

Take the Natural logarithmic to base 31 of both sides

Log_31 (31)ⁿ = Log_31 (1,000,000,000)

n•Log_31 (31) = Log_31 (1,000,000,000)

Then, log_a (a) = 1

n = Log_31 (1,000,000,000)

Check attachment for better view

Then,

The correct answer is A