Question

Write an exponential equation:Growth: A = a(1 + r) Decay: A =a(1 - r)Initial value: $120 growth rate:7.25% time: 3 yearsSet up: 7.25=1Simplified equation:

Answer 1

Exponential equation

Initial explanation

If we apply the exponential equation to a finantial situation, were you invest some value of money and you receive (or loose) a percentage of it, then we will have that the equation will have the form:

`A=a(1\pm r)^t`

Its parts are:

- a: initial value

- r: growth or decreasing rate

- t: time

- A: total amount of money

Finding a simplified equation for this case

Then, in this case

- a = $120

- r = 7.25% = 7.25/100 = 0.0725

Since it is a growth rate then it is an addition +

- t = 2 years

- A: total amount of money

Replacing in the equation, we have that:

`\begin{gathered} A=a(1\pm r)^t \\ \downarrow \\ A=120(1+0.0725)^2 \end{gathered}`

Total amount of money after two years

If we solve the previous simplified equation, we have that:

`\begin{gathered} A=120(1+0.0725)^2 \\ \downarrow \\ A=120(1.0725)^2 \\ A=120\cdot1.50=138.03075 \end{gathered}`

After two years, the total amount of money (including the growth rate) is

$138.03075.