Question

Create an exponential to describe $100 at 2% interest, compounded annually, for x years. y=100(.98)^x y=100(.8)^x y=100(1.2)^x y=100(1.02)^x

Answer 1

The exponential to describe $100 at 2% interest, compounded annually, for x years is
`y=100(1.02)^(x)`

Solution:

Given that $ 100 at 2 % interest , compounded annually for "x" years

The formula for compound interest, including principal sum, is:

`A=P\left(1+(r)/(n)\right)^(n t)`

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested or borrowed for

Here in this sum,

P = $ 100

`r = 2 \% = (2)/(100) = 0.02`

number of years = x

Here given that compounded annually , so n = 1

Let "y" be the amount after "x" years

Substituting the values in formula we get,

`\begin{aligned}&y=100\left(1+(0.02)/(1)\right)^(1 * x)\\\\&y=100(1+0.02)^(x)\\\\&y=100(1.02)^(x)\end{aligned}`

Thus the exponential to describe is
`y=100(1.02)^(x)`