Question

consider the following functions which all have a value of 30 does each equation represent growth or decay

Answer 1

The general equation forms representing growth or decay is;

`\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}`

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%