The function that will represent the growth of the bacteria overtime is:
f(y) = 70 × 3ʸ
Definition of a function
A function is a mathematical representation which gives a better understanding of a written statement.
How to determine the function for the growth
From the question given above, we were told that:
- Initial amount is 70
- Amount triples every hour (i.e times 3)
Let f represent the growth
Let y represent the time.
Therefore, the function for the growth of the bacteria can be written as
f(y) = 70 × 3ʸ
Verification of the function
f(y) = 70 × 3ʸ
f(0) = 70 × 3⁰
f(0) = 70 × 1
f(0) = 70
- Time (y) = 1
- Growth (f) =?
f(y) = 70 × 3ʸ
f(1) = 70 × 3¹
f(1) = 70 × 3
f(1) = 210
- Time (y) = 2
- Growth (f) =?
f(y) = 70 × 3ʸ
f(2) = 70 × 3²
f(2) = 70 × 9
f(2) = 630
From the above illustrations, we can conclude that the function that represents the growth of the bacteria overtime is:
f(y) = 70 × 3ʸ
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