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KengaRu [80]
3 years ago
7

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
Mathematics
1 answer:
zysi [14]3 years ago
5 0

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

<h3><u>Solution:</u></h3>

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

<em><u>The formula for compound interest, including principal sum, is:</u></em>

A=P\left(1+\frac{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 \% = \frac{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+\frac{0.02}{1}\right)^{1 \times 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}

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