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23
Since it’s doubling for our question, we can say that f is 2, the initial population
Po would be 2000 and n would be 5 hours, therefore we can write it as: P =
2000(2)n (17) P = 2000(2)5 (18) P = 64000 (19)
This makes it easier, right? Similarly if the question changed to exponential
decay and instead of doubling, the population was halving the general formula
could’ve been written as:
P = 2000(1 2 ) n (20)
Here, it would half every time. If they said it was decrease by a factor of 3 then
it would’ve been:
P = 2000(1 3 ) n (21)
This same concept it also utilised in the compound interest formula: C = P(1 ±
r 100 ) n (22)
3 3 Surds
Surds are values in square roots that can’t be further simplified into a easier
form.
Let’s say we have square root of 40. If you put that in a calculator, it will,
instead of outputting √ 40 give you the answer 2√ 10. Why? .
The second form is the simplest form of √ 40. In this section we’ll learn how to
solve and simplify surds.
3.1 Simplifying Expressions involving surds
Let’s say we have a surd √ 60 and we have to simplify it. For any question, the
steps to be followed are:
1. For the number inside the square root, break it down into its factors as
simply as possible so for 60 we can write it sequentially in fragments as:
(a) 2 ∗ 30
(b) 2 ∗ 2 ∗ 15
(c) 2 ∗ 2 ∗ 3 ∗ 5 2.
Those numbers that appear in pairs, write them in exponent notation: so in the
case of 60 as the number ’2’ appears two times, we can write the factors as
22 ∗ 3 ∗ 5 3. The number that appeared in pairs and were subsequently put
into the exponent form, bring the single number out of the root so we write it
as:
2 p (3 ∗ 5) (23) 2 √ 15 (24)
Thus, this will be your final answer.