The general equation forms representing growth or decay is;
[tex]\begin{gathered} F=I(1+r)^{t\text{ }}orF=I(1-r)^t \\ F\text{ is future value} \\ I\text{ is initial value} \\ r\text{ is growth rate} \\ t\text{ is time} \\ (1-r)\text{ represents decay} \\ (1+r)\text{ represents growth} \end{gathered}[/tex]
So let us consider the equations;
a) f(t) = 30(1.04)^t
f(t) = 30(1+0.04)^t
It is growth as it is greater than 1 and the growth rate is 0.04 = 4/100 = 4%
b) p(x) = 30(0.65)^x
P(x) = 30(1-0.35)^x
it is decay as it is less than 1
Growth rate is 0.35 = 35/100 = 35%
c) A(x) = 30(1.10)^x
A(x) = 30(1 + 0.1)^x
it is growth as it is greater than 1
0.1 = 10/100 = 10%
d) h(t) = 30(0.98)^t
h(t) = 30(1-0.02)^t
It is decay since it is less than 1
growth rate is;
0.02 = 2/100 = 2%
e) s(t) = 30(0.77)^t
s(t) = 30(1-0.23)^t
it is decay as it is less than 1
0.23 is growth rate = 23/100 = 23%
f) B(t) = 30(1.2)^t
B(t) = 30(1+0.2)^t
It is growth since it is greater than 1
0.2 = 20/100 = 20%
