急 ! F4 Exponential Functions 1

(a) 2^(3x+3)=125
[2^(3x)](2^3)=5^3
2^(3x)=(5^3)/(2^3)
(2^x)^3=(5/2)^3
2^x=5/2

(b) From (a):
2^x=5/2
(2^x)^2=(5/2)^2
(2^2)^x=25/4
4^x=25/4
(4^x)^-1=(25/4)^-1
1/(4^x)=4/25
(1^x)/(4^x)=4/25
(1/4)^x=4/25


23.
(a) m=m0Xa^y
98.71=100Xa^30
a^30=98.71/100
log(a^30)=log(98.71/100)
30 log a=-5.638848X10^(-3)
log a=-1.879616X10^(-4)
a=0.9995673
a=0.99957 (correct to 5 sig. fig.)

(b) m=m0X0.9995673^y
If y=1000
m=m0X0.9995673^1000=0.6486943m0
m/m0=0.6486943=64.86943%
The percentage decrease in the mass is:
1-64.86943%
=35.13057%
=35.131% (correct to 5 sig. fig.)