Everything Maths Grade 11

2.3 CHAPTER 2. EXPONENTS

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(1.) 016e (2.) 016f

2.3 Exponentials in theReal World EMBE

In Grade 10 Finance, you used exponentials tocalculate different typesof interest, for exampleon a

savings account or on aloan and compound growth.

Example 3: Exponentials in the Real world

QUESTION

A type of bacteria has avery high exponential growth rate at 80% every hour. If there are 10

bacteria, determine howmany there will be in five hours, in one day andin one week?

SOLUTION

Step 1 : Population = Initial population× (1 + growth percentage)time period in hours

Therefore, in this case:

P opulation = 10(1,8)n, where n = number of hours

Step 2 : In 5 hours

P opulation = 10(1,8)^5 = 189

Step 3 : In 1 day = 24 hours

P opulation = 10(1,8)^24 = 13 382 588

Step 4 : in 1 week = 168 hours

P opulation = 10(1,8)^168 = 7, 687 × 1043

Note this answer is given in scientific notation as it is a very big number.