Page 36 - Spotlight A+ Form 4 & 5 Mathematics KSSM

Form
5
Chapter 8 Mathematical Modeling Mathematics
(a) Exponential growth model Use the constructed model to solve the problem.
The exponential function shows growth if y = 19 000(1 + 0.15) 9
a . 0 and b . 1.
The exponential growth model: = 66 839.6495
y ≈ 66 840
y = a(1 + r) t Thus, the population of the city in the 9th year is
66 840 people.
where a = the initial value
r = the growth rate Try questions 7 & 8 in Formative Zone 8.1
t = the time
y
Example 12
3
The value of a car worth RM350 000 will be
2
depreciated every year by 11%.
1 (a) If y represents the value of the car, in RM, for
t years, model the situation.
t (b) What is the value of the car after 9 years?
–2 –1 0 1
Solution:
(b) Exponential decay model (a) The initial value is 350 000, that is,
The exponential function shows decay if a = 350 000.
a . 0 and 0 , b , 1. The decay rate is 11%, that is, r = 0.11.
The exponential decay model: Thus, the exponential decay model is
y = 350 000(1 – 0.11) t
y = a(1 – r) t y = 350 000(0.89) t
9
where a = the initial value (b) y = 350 000(0.89)
= 122 624.7413

r = the decay rate y ≈ 122 624.74
t = the time

©PAN ASIA PUBLICATIONS
Thus, the value of the car after 9 years is

y RM122 624.74.
Try question 9 in Formative Zone 8.1
3
2
8. The compound interest model is the interest
1 calculated with the reference to the original
principal as well as the accumulated interest
t
–1 0 1 2 from the previous retention period.

9. The compound interest model:
r
1
Example 11 A(t) = P 1 + — 2 nt
n
The population of a city is expected to increase by
15% annually. The population of today is 19 000 where A(t) = the amount of savings after t years
people. State the model involved and hence find P = the principal of the savings
the population of the city in the 9th year. r = the yearly interest rate
n = the number of interests being
Solution: compound per year
The initial value is 19 000, that is, a = 19 000. t = the number of years
The growth rate is 15%, that is, r = 0.15.
Hence, the exponential growth model is
y = 19 000(1 + 0.15) t CHAP.
8

422 8.1.2 423

C08 SpotlightA+ Mathematics F5.indd 423 03/03/2021 4:59 PM