Respuesta :
The exponential to describe $100 at 2% interest, compounded annually, for x years is [tex]y=100(1.02)^{x}[/tex]
Solution:
Given that $ 100 at 2 % interest , compounded annually for "x" years
The formula for compound interest, including principal sum, is:
[tex]A=P\left(1+\frac{r}{n}\right)^{n t}[/tex]
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
[tex]r = 2 \% = \frac{2}{100} = 0.02[/tex]
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,
[tex]\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}[/tex]
Thus the exponential to describe is [tex]y=100(1.02)^{x}[/tex]
