Maths F4....24

24.
(a)
The amount she will get after n months
= $50000*[1 + (2.4/12)%]^n
= $50000*1.002^n

(b)
Interest > 8% * Principal
(Amount - Principal) > 8% * Principal
50000*1.002^n - 50000 > 8% * 50000
50000(1.002^n - 1) > 50000 * 0.08
1.002^n - 1 > 0.08
1.002^n > 1.08
log1.002^n > log1.08
n*log1.002 > log1.08
n > log1.08/log1.002
n > 38.52

Hence, it is at least 39 months later.


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25.
(a)
"Original" means t = 0

The original number of bacteria
= 40 * (2.03)^0
= 40

(b)
2 hours = 2 * 60 min = 120 min

The number of bacteria after 2 hours
= 40 * (2.03)^(0.02*120)
= 219

(c)
Percentage change
= [(New value - Original value)/Original value] * 100%
= [(219 - 40)/40] * 100%
= 448%