In a parenting magazine, Mrs. Smith read an advertisement about all the different ways that bleach can be used to kill bacteria. The advertisement claimed that some forms of bacteria triple in amount after each hour. Consider the situation where one bacterium is found on Mrs. Smith's countertop at home.

Question:

(a) How many bacteria would be found in 24 hours

(b) How many bacteria would be found in 2 days

(c) How long for 1000 bacteria to be found

(a) 282429536481 bacteria

(b) bacteria

(c) 6 days

Step-by-step explanation:

The question illustrates an exponential function

Where

--- i.e. triples

Solving (a): Bacteria in 24 hours

In this case:

Substitute , and

So:

bacteria

Solving (b): Bacteria in 2 days

So:

Substitute , and

So:

bacteria

Solving (c): How long for 1000 bacteria

In this case:

Substitute , and

So:

Take Log of both sides

This gives:

Make x the subject

Hence: It takes 6 days

$9.41

step-by-step explanation:

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